BanditRLlib
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7,581 indexed public and private declarations. The catalog is exhaustive for the supported declaration kinds; teaching chapters add detailed explanations to the major mathematical interfaces.

From a concept to reusable Lean

Every search result links to its exact statement, source location, module context, chapter explanation, and recorded dependency neighborhood.

flowchart LR
    Search["Search a mathematical concept"] --> Decl["Exact Lean declaration"]
    Decl --> Statement["Statement + namespace + source line"]
    Decl --> Module["Owning module"]
    Module --> Imports["Imported prerequisites"]
    Decl --> Consumers["Downstream declarations"]
    Statement --> Chapter["Teaching explanation in Book Map"]
    Chapter --> Map["Implementation status and missing obligations"]
How a BanditRLlib concept search leads to source, dependencies, consumers, and teaching context · editable Mermaid source

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DeclarationKindChapterModuleStatusSource
BanditRLProof.ETC.Spec structure ETC BanditRLProof.Algorithms.ETC Compiled BanditRLProof/Algorithms/ETC.lean:11
BanditRLProof.ETC.exploreArm definition ETC BanditRLProof.Algorithms.ETC Compiled BanditRLProof/Algorithms/ETC.lean:16
BanditRLProof.ETC.exploreArm_val theorem ETC BanditRLProof.Algorithms.ETC Compiled BanditRLProof/Algorithms/ETC.lean:19
BanditRLProof.ETC.exploreArm_eq_of_mod_eq theorem ETC BanditRLProof.Algorithms.ETC Compiled BanditRLProof/Algorithms/ETC.lean:22
BanditRLProof.ETC.exploreArm_eq_iff_mod_eq_val theorem ETC BanditRLProof.Algorithms.ETC Compiled BanditRLProof/Algorithms/ETC.lean:28
BanditRLProof.ETC.exploreArm_add_K theorem ETC BanditRLProof.Algorithms.ETC Compiled BanditRLProof/Algorithms/ETC.lean:37
BanditRLProof.ETC.CommitOracle structure ETC BanditRLProof.Algorithms.ETC Compiled BanditRLProof/Algorithms/ETC.lean:43
BanditRLProof.ETC.obligationNames definition ETC BanditRLProof.Algorithms.ETC Compiled BanditRLProof/Algorithms/ETC.lean:48
BanditRLProof.ETC.score_le_foldl_select theorem ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:18
BanditRLProof.ETC.argmax_cons_eq_some_foldl_rat_select theorem ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:72
BanditRLProof.ETC.argmaxCommitOracle definition ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:100
BanditRLProof.ETC.argmaxCommitOracle_argmax_finRange theorem ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:117
BanditRLProof.ETC.argmaxCommitOracle_encode_le_of_score_le theorem ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:136
BanditRLProof.ETC.argmaxCommitOracle_choose_spec theorem ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:157
BanditRLProof.ETC.argmaxCommitOracle_eq_arm_subset_empMean_ge_bestArm theorem ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:177
BanditRLProof.ETC.prob_argmaxCommitOracle_eq_arm_le_pairwise_tail theorem ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:201
BanditRLProof.ETC.wrong_commit_subset_exists_empMean_ge_bestArm_of_argmaxOracle theorem ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:230
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_pairwise_tail theorem ETC BanditRLProof.Algorithms.ETCArgmaxOracle Compiled BanditRLProof/Algorithms/ETCArgmaxOracle.lean:260
BanditRLProof.ETC.indep_centeredReward_succ_pastReward_iSup_infinitePi theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardInfinitePiSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardInfinitePiSource.lean:28
BanditRLProof.ETC.indep_centeredReward_succ_historyFiltrationSucc_infinitePi theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardInfinitePiSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardInfinitePiSource.lean:60
BanditRLProof.ETC.boundedRewardTraceSource_infinitePi_actionWithCommit theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardInfinitePiSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardInfinitePiSource.lean:96
BanditRLProof.ETC.centeredRewardCondSubGaussianWitnesses_of_infinitePi_bounded_actionMean_canonicalTail definition ETC BanditRLProof.Algorithms.ETCBoundedRewardInfinitePiSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardInfinitePiSource.lean:179
BanditRLProof.ETC.pairwiseEmpMeanTailContract_of_infinitePi_bounded_actionMean_condSubGaussian_canonicalTail theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardInfinitePiSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardInfinitePiSource.lean:223
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_centeredDiffSubGaussianTail_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardInfinitePiSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardInfinitePiSource.lean:267
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_centeredDiffSubGaussianTail_of_infinitePi_bounded_actionMean_condSubGaussian theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardInfinitePiSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardInfinitePiSource.lean:314
BanditRLProof.ETC.BoundedRewardTraceSource structure ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:23
BanditRLProof.ETC.centeredReward_integrable_of_boundedRewardTraceSource theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:60
BanditRLProof.ETC.centeredReward_integral_eq_zero_of_boundedRewardTraceSource_mean theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:86
BanditRLProof.ETC.measurable_centeredReward_actionWithCommit_historyFiltrationSucc theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:115
BanditRLProof.ETC.stronglyAdapted_centeredReward_actionWithCommit_historyFiltrationSucc theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:163
BanditRLProof.ETC.centeredReward_actionWithCommit_integrable_of_boundedRewardTraceSource theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:192
BanditRLProof.ETC.centeredReward_succ_condExp_historyFiltrationSucc_eq_zero_of_boundedRewardTraceSource theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:241
BanditRLProof.ETC.centeredReward_actionWithCommit_succMartingaleDifferencePrefix_of_boundedRewardTraceSource theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:294
BanditRLProof.ETC.centeredReward_hasSubgaussianMGF_of_boundedRewardTraceSource theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:342
BanditRLProof.ETC.centeredReward_succ_hasCondSubgaussianMGF_historyFiltrationSucc_of_boundedRewardTraceSource theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:376
BanditRLProof.ETC.centeredRewardCondSubGaussianWitnesses_of_boundedRewardTraceSource definition ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:437
BanditRLProof.ETC.pairwiseEmpMeanTailContract_of_boundedRewardTraceSource_condSubGaussian theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:501
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_pairwise_tail_of_boundedRewardTraceSource_condSubGaussian theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:550
BanditRLProof.ETC.centeredRewardCondSubGaussianWitnesses_of_boundedRewardTraceSource_canonicalTail definition ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:603
BanditRLProof.ETC.pairwiseEmpMeanTailContract_of_boundedRewardTraceSource_condSubGaussian_canonicalTail theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:639
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_centeredDiffSubGaussianTail_of_boundedRewardTraceSource_condSubGaussian theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:682
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_centeredDiffSubGaussianTail_of_boundedRewardTraceSource theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSource Compiled BanditRLProof/Algorithms/ETCBoundedRewardSource.lean:723
BanditRLProof.ETC.centeredRewardBoundVarianceProxy definition ETC BanditRLProof.Algorithms.ETCBoundedRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCBoundedRewardSubGaussian.lean:19
BanditRLProof.ETC.centeredReward_integrable_of_mem_Icc theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCBoundedRewardSubGaussian.lean:32
BanditRLProof.ETC.centeredReward_integral_eq_zero_of_integral_eq_mean theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCBoundedRewardSubGaussian.lean:56
BanditRLProof.ETC.centeredReward_integral_eq_zero_of_mem_Icc_integral_eq_mean theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCBoundedRewardSubGaussian.lean:103
BanditRLProof.ETC.centeredReward_hasSubgaussianMGF_of_mem_Icc_integral_eq_mean theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCBoundedRewardSubGaussian.lean:138
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_centeredDiffSubGaussianTail_of_reward_iIndepFun_bounded_centered theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCBoundedRewardSubGaussian.lean:177
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_centeredDiffSubGaussianTail_of_reward_iIndepFun_action_centeredReward_subG theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCBoundedRewardSubGaussian.lean:236
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_centeredDiffSubGaussianTail_of_reward_iIndepFun_action_bounded_centered theorem ETC BanditRLProof.Algorithms.ETCBoundedRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCBoundedRewardSubGaussian.lean:290
BanditRLProof.ETC.centeredDiffSubGaussianTail definition ETC BanditRLProof.Algorithms.ETCCenteredDiffCanonicalTail Compiled BanditRLProof/Algorithms/ETCCenteredDiffCanonicalTail.lean:22
BanditRLProof.ETC.centeredDiffSubGaussianWitnesses_of_indep_subG definition ETC BanditRLProof.Algorithms.ETCCenteredDiffCanonicalTail Compiled BanditRLProof/Algorithms/ETCCenteredDiffCanonicalTail.lean:43
BanditRLProof.ETC.pairwiseEmpMeanTailContract_of_centeredDiff_indep_subG theorem ETC BanditRLProof.Algorithms.ETCCenteredDiffCanonicalTail Compiled BanditRLProof/Algorithms/ETCCenteredDiffCanonicalTail.lean:83
BanditRLProof.ETC.iIndepFun_centeredPairwiseRewardDiff_of_iIndepFun_reward theorem ETC BanditRLProof.Algorithms.ETCCenteredDiffRewardIndependence Compiled BanditRLProof/Algorithms/ETCCenteredDiffRewardIndependence.lean:26
BanditRLProof.ETC.centeredPairwiseRewardDiffVarianceProxy definition ETC BanditRLProof.Algorithms.ETCCenteredDiffRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCCenteredDiffRewardSubGaussian.lean:22
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasSubgaussianMGF_of_centeredReward theorem ETC BanditRLProof.Algorithms.ETCCenteredDiffRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCCenteredDiffRewardSubGaussian.lean:43
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_centeredDiffSubGaussianTail_of_reward_iIndepFun_centeredReward_subG theorem ETC BanditRLProof.Algorithms.ETCCenteredDiffRewardSubGaussian Compiled BanditRLProof/Algorithms/ETCCenteredDiffRewardSubGaussian.lean:108
BanditRLProof.ETC.CenteredDiffSubGaussianWitnesses structure ETC BanditRLProof.Algorithms.ETCCenteredDiffSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCenteredDiffSubGaussianWitnesses.lean:25
BanditRLProof.ETC.pairwiseEmpMeanTailContract_of_centeredDiffSubGaussianWitnesses theorem ETC BanditRLProof.Algorithms.ETCCenteredDiffSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCenteredDiffSubGaussianWitnesses.lean:66
BanditRLProof.ETC.measurable_centeredPairwiseRewardDiff_historyFiltrationSucc theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:28
BanditRLProof.ETC.stronglyAdapted_centeredPairwiseRewardDiff_historyFiltrationSucc theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:82
BanditRLProof.ETC.centeredReward_condExp_eq_zero_of_indep theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:116
BanditRLProof.ETC.centeredReward_condExp_historyFiltrationSucc_eq_zero_of_indep theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:172
BanditRLProof.ETC.indep_centeredReward_succ_pastReward_iSup_of_iIndepFun_reward theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:243
BanditRLProof.ETC.historyFiltrationSucc_actionWithCommit_le_pastReward_iSup theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:327
BanditRLProof.ETC.indep_centeredReward_succ_historyFiltrationSucc_of_iIndepFun_reward theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:433
BanditRLProof.ETC.centeredReward_succ_condExp_historyFiltrationSucc_eq_zero_of_indep theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:475
BanditRLProof.ETC.centeredReward_succ_condExp_historyFiltrationSucc_eq_zero_of_iIndepFun_reward theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:544
BanditRLProof.ETC.hasCondSubgaussianMGF_of_indep_comap theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:592
BanditRLProof.ETC.centeredReward_succ_hasCondSubgaussianMGF_historyFiltrationSucc_of_iIndepFun_reward theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:723
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasSubgaussianMGF_of_action_miss theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:793
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasCondSubgaussianMGF_of_action_miss theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:820
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasCondSubgaussianMGF_historyFiltrationSucc_of_action_miss theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:849
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasCondSubgaussianMGF_of_action_eq_arm theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:902
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasCondSubgaussianMGF_of_action_eq_bestArm theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:943
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasCondSubgaussianMGF_historyFiltrationSucc_of_action_eq_arm theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:983
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasCondSubgaussianMGF_historyFiltrationSucc_of_action_eq_bestArm theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:1046
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasCondSubgaussianMGF_of_centeredReward theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:1117
BanditRLProof.ETC.centeredPairwiseRewardDiff_hasCondSubgaussianMGF_historyFiltrationSucc_of_centeredReward theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:1194
BanditRLProof.ETC.CenteredRewardCondSubGaussianWitnesses structure ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:1266
BanditRLProof.ETC.CenteredDiffCondSubGaussianWitnesses structure ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:1325
BanditRLProof.ETC.centeredDiffCondSubGaussianWitnesses_of_centeredRewardCondSubGaussianWitnesses definition ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:1377
BanditRLProof.ETC.pairwiseEmpMeanTailContract_of_centeredDiffCondSubGaussianWitnesses theorem ETC BanditRLProof.Algorithms.ETCCondSubGaussianWitnesses Compiled BanditRLProof/Algorithms/ETCCondSubGaussianWitnesses.lean:1442
BanditRLProof.ETC.pullCount_exploreArm_K_eq_one theorem ETC BanditRLProof.Algorithms.ETCCountLemmas Compiled BanditRLProof/Algorithms/ETCCountLemmas.lean:22
BanditRLProof.ETC.pullCount_exploreArm_add_K_eq_add_one theorem ETC BanditRLProof.Algorithms.ETCCountLemmas Compiled BanditRLProof/Algorithms/ETCCountLemmas.lean:58
BanditRLProof.ETC.pullCount_exploreArm_mul_K_eq theorem ETC BanditRLProof.Algorithms.ETCCountLemmas Compiled BanditRLProof/Algorithms/ETCCountLemmas.lean:86
BanditRLProof.ETC.pullCount_exploreArm_explorationPulls_mul_K_eq theorem ETC BanditRLProof.Algorithms.ETCCountLemmas Compiled BanditRLProof/Algorithms/ETCCountLemmas.lean:105
BanditRLProof.ETC.empMeanAtExploration definition ETC BanditRLProof.Algorithms.ETCEmpiricalMean Compiled BanditRLProof/Algorithms/ETCEmpiricalMean.lean:24
BanditRLProof.ETC.empMeanAtExploration_eq_of_eq_on_prefix theorem ETC BanditRLProof.Algorithms.ETCEmpiricalMean Compiled BanditRLProof/Algorithms/ETCEmpiricalMean.lean:39
BanditRLProof.ETC.empMeanAtExploration_completeRewardTrace_eq_of_explorationHorizon_le theorem ETC BanditRLProof.Algorithms.ETCEmpiricalMean Compiled BanditRLProof/Algorithms/ETCEmpiricalMean.lean:69
BanditRLProof.ETC.empMeanAtExploration_eq_sumRewards_div_explorationPulls theorem ETC BanditRLProof.Algorithms.ETCEmpiricalMean Compiled BanditRLProof/Algorithms/ETCEmpiricalMean.lean:88
BanditRLProof.ETC.empMeanAtExploration_le_iff_sumRewards_le_of_explorationPulls_pos theorem ETC BanditRLProof.Algorithms.ETCEmpiricalMean Compiled BanditRLProof/Algorithms/ETCEmpiricalMean.lean:107
BanditRLProof.ETC.empMeanAtExploration_ge_best_event_subset_sumRewards_tail_event_of_imp theorem ETC BanditRLProof.Algorithms.ETCEmpiricalMean Compiled BanditRLProof/Algorithms/ETCEmpiricalMean.lean:133
BanditRLProof.ETC.measurable_sumRewards_actionWithCommit_exploration theorem ETC BanditRLProof.Algorithms.ETCEmpiricalMeanMeasurability Compiled BanditRLProof/Algorithms/ETCEmpiricalMeanMeasurability.lean:27
BanditRLProof.ETC.measurable_empMeanAtExploration_of_measurable_div_const theorem ETC BanditRLProof.Algorithms.ETCEmpiricalMeanMeasurability Compiled BanditRLProof/Algorithms/ETCEmpiricalMeanMeasurability.lean:59
BanditRLProof.ETC.measurable_empMeanAtExploration theorem ETC BanditRLProof.Algorithms.ETCEmpiricalMeanMeasurability Compiled BanditRLProof/Algorithms/ETCEmpiricalMeanMeasurability.lean:93
BanditRLProof.ETC.measurable_empMeanAtExploration_coordinates theorem ETC BanditRLProof.Algorithms.ETCEmpiricalMeanMeasurability Compiled BanditRLProof/Algorithms/ETCEmpiricalMeanMeasurability.lean:118
BanditRLProof.ETC.sum_centeredPairwiseRewardDiffVarianceProxy_const_eq_two_mul theorem ETC BanditRLProof.Algorithms.ETCExactSubGaussianTail Compiled BanditRLProof/Algorithms/ETCExactSubGaussianTail.lean:23
BanditRLProof.ETC.centeredPairwiseGapThreshold_eq_explorationPulls_mul_gap theorem ETC BanditRLProof.Algorithms.ETCExactSubGaussianTail Compiled BanditRLProof/Algorithms/ETCExactSubGaussianTail.lean:79
BanditRLProof.ETC.canonicalSubGaussianArmPairwiseTailReal_eq_exp_neg_explorationPulls_mul_gap_sq_div_four_mul theorem ETC BanditRLProof.Algorithms.ETCExactSubGaussianTail Compiled BanditRLProof/Algorithms/ETCExactSubGaussianTail.lean:99
BanditRLProof.ETC.real_measure_explorationArgmaxCommit_eq_arm_le_exp_neg_explorationPulls_mul_gap_sq_div_four_mul_of_armLaws theorem ETC BanditRLProof.Algorithms.ETCExactSubGaussianTail Compiled BanditRLProof/Algorithms/ETCExactSubGaussianTail.lean:152
BanditRLProof.ETC.integral_real_pullCount_explorationArgmaxAction_le_exploration_add_remaining_mul_exp_of_armLaws theorem ETC BanditRLProof.Algorithms.ETCExactSubGaussianTail Compiled BanditRLProof/Algorithms/ETCExactSubGaussianTail.lean:207
BanditRLProof.ETC.integrable_real_pullCount_actionWithCommit_choice_of_measurable_commit theorem ETC BanditRLProof.Algorithms.ETCExpectedPullCount Compiled BanditRLProof/Algorithms/ETCExpectedPullCount.lean:30
BanditRLProof.ETC.integral_real_pullCount_actionWithCommit_choice_eq_exploration_add_suffix_mul_commit_prob theorem ETC BanditRLProof.Algorithms.ETCExpectedPullCount Compiled BanditRLProof/Algorithms/ETCExpectedPullCount.lean:69
BanditRLProof.ETC.integral_real_pullCount_actionWithCommit_choice_eq_exploration_add_remaining_mul_commit_prob theorem ETC BanditRLProof.Algorithms.ETCExpectedPullCount Compiled BanditRLProof/Algorithms/ETCExpectedPullCount.lean:116
BanditRLProof.ETC.integral_real_pullCount_actionWithCommit_choice_le_exploration_add_remaining_mul_of_commit_prob_le theorem ETC BanditRLProof.Algorithms.ETCExpectedPullCount Compiled BanditRLProof/Algorithms/ETCExpectedPullCount.lean:163
BanditRLProof.ETC.lintegral_ofReal_pseudoRegret_actionWithCommit_choice_le_exploration_add_suffix_badGap_prob theorem ETC BanditRLProof.Algorithms.ETCExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCExpectedRegretAssembly.lean:33
BanditRLProof.ETC.integrable_real_pseudoRegret_actionWithCommit_choice_of_measurable_commit theorem ETC BanditRLProof.Algorithms.ETCExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCExpectedRegretAssembly.lean:162
BanditRLProof.ETC.integral_real_pseudoRegret_actionWithCommit_choice_le_exploration_add_suffix_sum_gap_mul_commit_prob theorem ETC BanditRLProof.Algorithms.ETCExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCExpectedRegretAssembly.lean:208
BanditRLProof.ETC.integral_real_pseudoRegret_actionWithCommit_choice_le_exploration_add_suffix_badGap_prob theorem ETC BanditRLProof.Algorithms.ETCExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCExpectedRegretAssembly.lean:339
BanditRLProof.RewardKernel.pair_map_eq_compProd_of_map_eq_of_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:43
BanditRLProof.RewardKernel.condDistrib_pair_ae_eq_compProd_of_split theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:72
BanditRLProof.RewardKernel.condDistrib_ae_eq_const_of_comp theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:143
BanditRLProof.RewardKernel.map_eq_of_condDistrib_ae_eq_const theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:195
BanditRLProof.RewardKernel.condDistrib_ae_eq_const_of_ae_eq_selected theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:236
BanditRLProof.ETC.finiteArmCenteredRewardKernelLaw_of_hasSubgaussianMGF definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:280
BanditRLProof.ETC.finiteArmBoundedCenteredRewardKernelLaw definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:332
BanditRLProof.ETC.explorationArgmaxHistory_centeredReward_succ_hasCondSubgaussianMGF_of_boundedArmLaws theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:393
BanditRLProof.ETC.explorationArgmaxHistory_centeredReward_succ_hasCondSubgaussianMGF_of_armLaws theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:472
BanditRLProof.ETC.explorationArgmaxHistory_centeredRewardProcess_sum_tail_ennreal_of_boundedArmLaws theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:550
BanditRLProof.ETC.explorationArgmaxHistory_centeredRewardCondSubGaussianWitnesses_of_boundedArmLaws definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:736
BanditRLProof.ETC.explorationArgmaxHistory_centeredRewardCondSubGaussianWitnesses_of_armLaws definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:905
BanditRLProof.ETC.explorationArgmaxHistory_pairwiseEmpMeanTailContract_of_boundedArmLaws theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1058
BanditRLProof.ETC.explorationArgmaxHistory_pairwiseEmpMeanTailContract_of_armLaws theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1130
BanditRLProof.ETC.explorationArgmaxHistory_prob_commit_eq_arm_le_pairwiseTail_of_armLaws theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1198
BanditRLProof.ETC.explorationArgmaxHistory_prob_commit_eq_arm_le_pairwiseTail_of_boundedArmLaws theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1271
BanditRLProof.ETC.explorationArgmaxHistory_prob_wrongCommit_le_pairwiseTailSum_of_boundedArmLaws theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1348
BanditRLProof.ETC.canonicalBoundedArmWrongCommitTailBudget definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1421
BanditRLProof.ETC.canonicalBoundedArmWrongCommitTailBudgetReal definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1433
BanditRLProof.ETC.canonicalBoundedArmMaxGapIntegralRegretBoundReal definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1444
BanditRLProof.ETC.canonicalBoundedArmPairwiseTailReal definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1457
BanditRLProof.ETC.canonicalBoundedArmPerArmIntegralRegretBoundReal definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1473
BanditRLProof.ETC.canonicalSubGaussianArmPairwiseTailReal definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1486
BanditRLProof.ETC.canonicalSubGaussianArmPerArmIntegralRegretBoundReal definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1501
BanditRLProof.ETC.real_measure_explorationArgmaxCommit_eq_arm_le_canonicalSubGaussianArmPairwiseTailReal theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1520
BanditRLProof.ETC.real_measure_explorationArgmaxCommit_eq_arm_le_canonicalBoundedArmPairwiseTailReal theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1591
BanditRLProof.ETC.real_measure_explorationArgmaxCommit_ne_bestArm_le_canonicalBoundedArmWrongCommitTailBudgetReal theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1664
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_le_canonicalBoundedArmMaxGapIntegralRegretBoundReal theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1736
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_le_canonicalBoundedArmPerArmIntegralRegretBoundReal theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1855
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_le_canonicalSubGaussianArmPerArmIntegralRegretBoundReal theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:1980
BanditRLProof.ETC.explorationArgmaxPrefixRegretReal definition ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2104
BanditRLProof.ETC.measurable_explorationArgmaxPrefixRegretReal theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2113
BanditRLProof.ETC.explorationArgmaxPrefixRegretReal_finiteRewardHistoryOfTrace theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2169
BanditRLProof.ETC.explorationArgmaxPrefixRegretReal_finiteRewardHistoryOfTrace_generated theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2196
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_eq_of_explorationPrefix_map_eq theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2219
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_le_canonicalBoundedArmMaxGapIntegralRegretBoundReal_of_explorationPrefix_map_eq theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2301
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_le_canonicalBoundedArmPerArmIntegralRegretBoundReal_of_explorationPrefix_map_eq theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2422
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_le_canonicalSubGaussianArmPerArmIntegralRegretBoundReal_of_explorationPrefix_map_eq theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2509
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalBoundedArmMaxGapIntegralRegretBoundReal_of_initial_map_eq_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2597
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalBoundedArmPerArmIntegralRegretBoundReal_of_initial_map_eq_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2722
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalSubGaussianArmPerArmIntegralRegretBoundReal_of_initial_map_eq_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2846
BanditRLProof.ETC.explorationArgmaxHistory_stepKernel_apply_eq_exploreArmLaw_of_lt theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:2969
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalBoundedArmMaxGapIntegralRegretBoundReal_of_initial_map_eq_explorationArm_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:3001
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalBoundedArmPerArmIntegralRegretBoundReal_of_initial_map_eq_explorationArm_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:3064
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalSubGaussianArmPerArmIntegralRegretBoundReal_of_initial_map_eq_explorationArm_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:3127
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalBoundedArmMaxGapIntegralRegretBoundReal_of_actionRewardHistory_explorationArm_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:3191
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalBoundedArmPerArmIntegralRegretBoundReal_of_actionRewardHistory_explorationArm_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:3284
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalSubGaussianArmPerArmIntegralRegretBoundReal_of_actionRewardHistory_explorationArm_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:3378
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalBoundedArmMaxGapIntegralRegretBoundReal_of_actionDependent_actionRewardHistory_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:3471
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalBoundedArmPerArmIntegralRegretBoundReal_of_actionDependent_actionRewardHistory_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:3566
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxGeneratedAction_reward_le_canonicalSubGaussianArmPerArmIntegralRegretBoundReal_of_actionDependent_actionRewardHistory_condDistrib theorem ETC BanditRLProof.Algorithms.ETCFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/ETCFiniteArmRewardLaw.lean:3661
BanditRLProof.ETC.explorationArgmaxHistoryState definition ETC BanditRLProof.Algorithms.ETCGeneratedHistoryPolicy Compiled BanditRLProof/Algorithms/ETCGeneratedHistoryPolicy.lean:27
BanditRLProof.ETC.measurable_explorationArgmaxHistoryState theorem ETC BanditRLProof.Algorithms.ETCGeneratedHistoryPolicy Compiled BanditRLProof/Algorithms/ETCGeneratedHistoryPolicy.lean:33
BanditRLProof.ETC.explorationArgmaxHistoryPolicy definition ETC BanditRLProof.Algorithms.ETCGeneratedHistoryPolicy Compiled BanditRLProof/Algorithms/ETCGeneratedHistoryPolicy.lean:51
BanditRLProof.ETC.explorationArgmaxGeneratedAction definition ETC BanditRLProof.Algorithms.ETCGeneratedHistoryPolicy Compiled BanditRLProof/Algorithms/ETCGeneratedHistoryPolicy.lean:77
BanditRLProof.ETC.explorationArgmaxGeneratedAction_eq_explorationArgmaxAction theorem ETC BanditRLProof.Algorithms.ETCGeneratedHistoryPolicy Compiled BanditRLProof/Algorithms/ETCGeneratedHistoryPolicy.lean:95
BanditRLProof.ETC.explorationArgmaxGeneratedAction_eq_actionWithCommit_of_lt theorem ETC BanditRLProof.Algorithms.ETCGeneratedHistoryPolicy Compiled BanditRLProof/Algorithms/ETCGeneratedHistoryPolicy.lean:143
BanditRLProof.ETC.explorationArgmaxGeneratedActionPartialTrajectoryPairLawSource_trajMeasure definition ETC BanditRLProof.Algorithms.ETCGeneratedHistoryPolicy Compiled BanditRLProof/Algorithms/ETCGeneratedHistoryPolicy.lean:180
BanditRLProof.ETC.explorationArgmaxHistory_centeredReward_succ_hasCondSubgaussianMGF_trajMeasure theorem ETC BanditRLProof.Algorithms.ETCGeneratedHistoryPolicy Compiled BanditRLProof/Algorithms/ETCGeneratedHistoryPolicy.lean:227
BanditRLProof.ETC.fixedProductArgmaxCommit definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:26
BanditRLProof.ETC.fixedProductArgmaxAction definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:40
BanditRLProof.ETC.fixedProductMaxGapLintegralRegretBound definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:56
BanditRLProof.ETC.fixedProductWrongCommitTailBudget definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:79
BanditRLProof.ETC.fixedProductBadGapLintegralRegretBound definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:99
BanditRLProof.ETC.fixedProductSumGapLintegralRegretBound definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:124
BanditRLProof.ETC.fixedProductWrongCommitTailBudgetReal definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:140
BanditRLProof.ETC.fixedProductBadGapIntegralRegretBoundReal definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:152
BanditRLProof.ETC.fixedProductSumGapIntegralRegretBoundReal definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:179
BanditRLProof.ETC.fixedProductMaxGapIntegralRegretBoundReal definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:201
BanditRLProof.ETC.explorationArgmaxCommit definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:217
BanditRLProof.ETC.explorationArgmaxAction definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:228
BanditRLProof.ETC.explorationMaxGapIntegralRegretBoundReal definition ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:239
BanditRLProof.ETC.lintegral_ofReal_pseudoRegret_argmaxCommitOracle_actionWithCommit_le_exploration_add_suffix_badGap_prob_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:258
BanditRLProof.ETC.lintegral_ofReal_pseudoRegret_fixedProductArgmaxAction_le_fixedProductBadGapLintegralRegretBound_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:378
BanditRLProof.ETC.lintegral_ofReal_pseudoRegret_fixedProductArgmaxAction_le_fixedProductSumGapLintegralRegretBound_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:438
BanditRLProof.ETC.real_measure_fixedProductArgmaxCommit_ne_bestArm_le_fixedProductWrongCommitTailBudgetReal_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:501
BanditRLProof.ETC.integral_real_pseudoRegret_argmaxCommitOracle_actionWithCommit_le_exploration_add_suffix_badGap_prob_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:567
BanditRLProof.ETC.integral_real_pseudoRegret_fixedProductArgmaxAction_le_fixedProductBadGapIntegralRegretBoundReal_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:705
BanditRLProof.ETC.integral_real_pseudoRegret_argmaxCommitOracle_actionWithCommit_le_exploration_add_suffix_sumGap_prob_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:766
BanditRLProof.ETC.integral_real_pseudoRegret_fixedProductArgmaxAction_le_fixedProductSumGapIntegralRegretBoundReal_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:832
BanditRLProof.ETC.integral_real_pseudoRegret_argmaxCommitOracle_actionWithCommit_le_exploration_add_suffix_maxGap_prob_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:885
BanditRLProof.ETC.integral_real_pseudoRegret_fixedProductArgmaxAction_le_fixedProductMaxGapIntegralRegretBoundReal_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:945
BanditRLProof.ETC.integral_real_pseudoRegret_explorationArgmaxAction_le_explorationMaxGapIntegralRegretBoundReal_of_infinitePi_bounded_exploreMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:998
BanditRLProof.ETC.lintegral_ofReal_pseudoRegret_argmaxCommitOracle_actionWithCommit_le_exploration_add_suffix_sumGap_prob_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:1061
BanditRLProof.ETC.lintegral_ofReal_pseudoRegret_argmaxCommitOracle_actionWithCommit_le_exploration_add_suffix_maxGap_prob_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:1136
BanditRLProof.ETC.lintegral_ofReal_pseudoRegret_fixedProductArgmaxAction_le_fixedProductMaxGapLintegralRegretBound_of_infinitePi_bounded_actionMean theorem ETC BanditRLProof.Algorithms.ETCInfinitePiExpectedRegretAssembly Compiled BanditRLProof/Algorithms/ETCInfinitePiExpectedRegretAssembly.lean:1204
BanditRLProof.ETC.measurableSet_commitArm_ne_bestArm theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:31
BanditRLProof.ETC.measurable_empMeanVector_of_forall_measurable theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:55
BanditRLProof.ETC.measurable_commitOracle_choose_of_measurable_empMeanVector theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:76
BanditRLProof.ETC.measurable_commitOracle_choose_of_forall_measurable_empMean theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:104
BanditRLProof.ETC.measurableSet_commitOracle_ne_bestArm theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:136
BanditRLProof.ETC.measurableSet_commitOracle_ne_bestArm_of_forall_measurable_empMean theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:165
BanditRLProof.ETC.measurableSet_empMean_ge_empMean theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:202
BanditRLProof.ETC.measurableSet_exists_ne_bestArm_empMean_ge_bestArm theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:222
BanditRLProof.ETC.wrong_commit_subset_exists_empMean_ge_bestArm theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:270
BanditRLProof.ETC.wrong_commit_subset_exists_empMean_ge_bestArm_of_commitOracle theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:298
BanditRLProof.ETC.prob_commitArm_ne_bestArm_le_wrong_mean_events_of_subset theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:330
BanditRLProof.ETC.prob_exists_ne_bestArm_empMean_ge_bestArm_le_sum theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:357
BanditRLProof.ETC.prob_commitArm_ne_bestArm_le_sum_wrong_mean_events theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:398
BanditRLProof.ETC.prob_commitArm_ne_bestArm_le_sum_pairwise_tail theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:427
BanditRLProof.ETC.prob_commitOracle_ne_bestArm_le_sum_pairwise_tail theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:487
BanditRLProof.ETC.prob_commitArm_ne_bestArm_le_sum_nonbest_pairwise_tail theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:525
BanditRLProof.ETC.prob_commitArm_ne_bestArm_le_filtered_sum_pairwise_tail theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:589
BanditRLProof.ETC.prob_commitOracle_ne_bestArm_le_filtered_sum_pairwise_tail theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:639
BanditRLProof.ETC.prob_commitOracle_ne_bestArm_le_sum_nonbest_pairwise_tail theorem ETC BanditRLProof.Algorithms.ETCMeasurability Compiled BanditRLProof/Algorithms/ETCMeasurability.lean:681
BanditRLProof.ETC.pairwiseEmpMeanTailContract_of_centered_subGaussian_event_bounds theorem ETC BanditRLProof.Algorithms.ETCPairwiseCenteredSubGaussianTail Compiled BanditRLProof/Algorithms/ETCPairwiseCenteredSubGaussianTail.lean:30
BanditRLProof.ETC.pairwiseEmpMeanTailContract_of_subGaussian_event_bounds theorem ETC BanditRLProof.Algorithms.ETCPairwiseSubGaussianTail Compiled BanditRLProof/Algorithms/ETCPairwiseSubGaussianTail.lean:25
BanditRLProof.ETC.PairwiseEmpMeanTailContract structure ETC BanditRLProof.Algorithms.ETCPairwiseTailContract Compiled BanditRLProof/Algorithms/ETCPairwiseTailContract.lean:24
BanditRLProof.ETC.prob_argmaxCommitOracle_eq_arm_le_pairwise_tail_of_contract theorem ETC BanditRLProof.Algorithms.ETCPairwiseTailContract Compiled BanditRLProof/Algorithms/ETCPairwiseTailContract.lean:48
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_pairwise_tail_of_contract theorem ETC BanditRLProof.Algorithms.ETCPairwiseTailContract Compiled BanditRLProof/Algorithms/ETCPairwiseTailContract.lean:83
BanditRLProof.ETC.ratArmLawRealKernel definition ETC BanditRLProof.Algorithms.ETCRatArmLawRealKernel Compiled BanditRLProof/Algorithms/ETCRatArmLawRealKernel.lean:24
BanditRLProof.ETC.ratArmLawRealKernel_apply theorem ETC BanditRLProof.Algorithms.ETCRatArmLawRealKernel Compiled BanditRLProof/Algorithms/ETCRatArmLawRealKernel.lean:32
BanditRLProof.ETC.isMarkovKernel_ratArmLawRealKernel theorem ETC BanditRLProof.Algorithms.ETCRatArmLawRealKernel Compiled BanditRLProof/Algorithms/ETCRatArmLawRealKernel.lean:40
BanditRLProof.ETC.realKernelMean_ratArmLawRealKernel_eq_integral_cast theorem ETC BanditRLProof.Algorithms.ETCRatArmLawRealKernel Compiled BanditRLProof/Algorithms/ETCRatArmLawRealKernel.lean:53
BanditRLProof.ETC.realKernelMean_ratArmLawRealKernel_eq_modelMean theorem ETC BanditRLProof.Algorithms.ETCRatArmLawRealKernel Compiled BanditRLProof/Algorithms/ETCRatArmLawRealKernel.lean:65
BanditRLProof.ETC.ciSup_modelMean_cast_eq_bestArm theorem ETC BanditRLProof.Algorithms.ETCRatArmLawRealKernel Compiled BanditRLProof/Algorithms/ETCRatArmLawRealKernel.lean:78
BanditRLProof.ETC.realKernelGap_ratArmLawRealKernel_eq_modelGap theorem ETC BanditRLProof.Algorithms.ETCRatArmLawRealKernel Compiled BanditRLProof/Algorithms/ETCRatArmLawRealKernel.lean:90
BanditRLProof.ETC.integral_realKernelRegret_explorationArgmaxAction_le_exact_sum_of_armLaws theorem ETC BanditRLProof.Algorithms.ETCRatArmLawRealKernel Compiled BanditRLProof/Algorithms/ETCRatArmLawRealKernel.lean:115
BanditRLProof.ETC.argmax_cons_eq_some_foldl_real_select theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:19
BanditRLProof.ETC.realArgmaxCommit_argmax_finRange theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:41
BanditRLProof.ETC.realArgmaxCommit_encode_le_of_score_le theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:53
BanditRLProof.ETC.RealEncodedArgmaxCandidate definition ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:65
BanditRLProof.ETC.exists_realEncodedArgmaxCandidate theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:71
BanditRLProof.ETC.realLeastEncodedArgmaxIndex definition ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:79
BanditRLProof.ETC.realLeastEncodedArgmaxIndex_candidate theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:84
BanditRLProof.ETC.realLeastEncodedArgmax definition ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:93
BanditRLProof.ETC.realLeastEncodedArgmax_encode_eq_index theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:97
BanditRLProof.ETC.realLeastEncodedArgmax_spec theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:104
BanditRLProof.ETC.realLeastEncodedArgmax_encode_le_of_isMax theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:110
BanditRLProof.ETC.realLeastEncodedArgmax_eq_realArgmaxCommit theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:123
BanditRLProof.ETC.eventually_realExplorationArgmaxAction_eq_of_roundRobin_leastEncodedCommit_persist theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:147
BanditRLProof.ETC.integral_realKernelRegret_externalAction_le_exact_sum_of_actionDependent_actionRewardHistory_condDistrib_of_leastEncodedCommit_persist theorem ETC BanditRLProof.Algorithms.ETCRealArgmaxTie Compiled BanditRLProof/Algorithms/ETCRealArgmaxTie.lean:211
BanditRLProof.ETC.realEmpMeanAtExploration definition ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:22
BanditRLProof.ETC.realEmpMeanAtExploration_eq_sumRewards_div_explorationPulls theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:30
BanditRLProof.ETC.measurable_realEmpMeanAtExploration theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:41
BanditRLProof.ETC.real_score_le_foldl_select theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:64
BanditRLProof.ETC.realArgmaxCommit definition ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:107
BanditRLProof.ETC.realArgmaxCommit_spec theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:115
BanditRLProof.ETC.realArgmaxCommit_const theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:124
BanditRLProof.ETC.measurable_selected_real_score theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:128
BanditRLProof.ETC.measurable_foldl_real_select theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:149
BanditRLProof.ETC.measurable_realArgmaxCommit_of_forall_measurable theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:185
BanditRLProof.ETC.realExplorationArgmaxCommit definition ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:197
BanditRLProof.ETC.realExplorationArgmaxAction definition ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:204
BanditRLProof.ETC.measurable_realExplorationArgmaxCommit theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:211
BanditRLProof.ETC.integral_real_pullCount_realExplorationArgmaxAction_eq_exploration_add_remaining_mul_commit_prob theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:226
BanditRLProof.ETC.integral_real_pullCount_realExplorationArgmaxAction_le_exploration_add_remaining_mul_of_commit_prob_le theorem ETC BanditRLProof.Algorithms.ETCRealEmpiricalMean Compiled BanditRLProof/Algorithms/ETCRealEmpiricalMean.lean:255
BanditRLProof.ETC.realHistoryPullCount definition ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:18
BanditRLProof.ETC.realHistorySumRewards definition ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:24
BanditRLProof.ETC.realHistoryEmpMean definition ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:30
BanditRLProof.ETC.realHistoryPullCount_finitePairHistoryOfTrace theorem ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:37
BanditRLProof.ETC.realHistorySumRewards_finitePairHistoryOfTrace theorem ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:68
BanditRLProof.ETC.realHistoryEmpMean_finitePairHistoryOfTrace theorem ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:87
BanditRLProof.ETC.pullCount_eq_of_eq_on_lt theorem ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:98
BanditRLProof.ETC.sumRewards_eq_of_action_eq_on_lt theorem ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:111
BanditRLProof.ETC.realHistoryEmpMean_exploration_eq_realEmpMeanAtExploration theorem ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:131
BanditRLProof.ETC.integral_realKernelRegret_externalAction_le_exact_sum_of_actionDependent_actionRewardHistory_condDistrib_of_historyLeastEncodedCommit_persist theorem ETC BanditRLProof.Algorithms.ETCRealHistoryScore Compiled BanditRLProof/Algorithms/ETCRealHistoryScore.lean:181
BanditRLProof.ETC.realKernelBestArm definition ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:27
BanditRLProof.ETC.realKernelMean_le_realKernelBestArm theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:32
BanditRLProof.ETC.ciSup_realKernelMean_eq_realKernelBestArm theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:39
BanditRLProof.ETC.realKernelGap_eq_realKernelBestArm_sub theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:50
BanditRLProof.ETC.realCenteredPairwiseRewardDiff definition ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:59
BanditRLProof.ETC.realCenteredPairwiseGapThreshold definition ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:70
BanditRLProof.ETC.realCenteredPairwiseRewardDiffVarianceProxy definition ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:76
BanditRLProof.ETC.real_selectedSubMean_sum_eq_sumRewards_sub_pullCount_mul theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:84
BanditRLProof.ETC.real_meanSubSelected_sum_eq_pullCount_mul_sub_sumRewards theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:109
BanditRLProof.ETC.real_sumRewards_le_imp_centered_pairwise_sum_ge theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:141
BanditRLProof.ETC.realExplorationArgmaxCommit_eq_arm_event_subset_centeredPairwise_sum_event theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:168
BanditRLProof.ETC.iIndepFun_realCenteredPairwiseRewardDiff_of_iIndepFun_reward theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:206
BanditRLProof.ETC.realCenteredPairwiseRewardDiff_hasSubgaussianMGF_of_centeredReward theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:226
BanditRLProof.ETC.sum_realCenteredPairwiseRewardDiffVarianceProxy_const_eq_two_mul theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:266
BanditRLProof.ETC.real_measure_realExplorationArgmaxCommit_eq_arm_le_exp_of_infinitePi_kernel theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:313
BanditRLProof.ETC.integral_real_pullCount_realExplorationArgmaxAction_le_exp_of_infinitePi_kernel theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:439
BanditRLProof.ETC.integral_realKernelRegret_realExplorationArgmaxAction_le_exact_sum_of_infinitePi_kernel theorem ETC BanditRLProof.Algorithms.ETCRealInfinitePiTail Compiled BanditRLProof/Algorithms/ETCRealInfinitePiTail.lean:479
BanditRLProof.ETC.RealStationaryETCSequence structure ETC BanditRLProof.Algorithms.ETCRealLMLCompat Compiled BanditRLProof/Algorithms/ETCRealLMLCompat.lean:27
BanditRLProof.ETC.regret_le_of_realStationaryETCSequence theorem ETC BanditRLProof.Algorithms.ETCRealLMLCompat Compiled BanditRLProof/Algorithms/ETCRealLMLCompat.lean:75
BanditRLProof.ETC.realExplorationRewardPrefix definition ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:21
BanditRLProof.ETC.realRewardTraceOfExplorationPrefix definition ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:26
BanditRLProof.ETC.realExplorationRewardPrefix_realRewardTraceOfExplorationPrefix theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:31
BanditRLProof.ETC.measurable_realExplorationRewardPrefix theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:42
BanditRLProof.ETC.measurable_realRewardTraceOfExplorationPrefix theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:47
BanditRLProof.ETC.measurable_realExplorationRewardPrefix_comp theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:58
BanditRLProof.ETC.sumRewards_eq_of_eq_on_lt theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:67
BanditRLProof.ETC.realEmpMeanAtExploration_eq_of_eq_on_exploration theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:79
BanditRLProof.ETC.realExplorationArgmaxCommit_eq_of_eq_on_exploration theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:94
BanditRLProof.ETC.realExplorationArgmaxCommit_realRewardTraceOf_prefix_eq theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:108
BanditRLProof.ETC.realExplorationArgmaxAction_realRewardTraceOf_prefix_eq theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:121
BanditRLProof.ETC.measurable_realKernelRegret_of_forall_measurable_action theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:132
BanditRLProof.ETC.realKernelRegretOfExplorationPrefix definition ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:149
BanditRLProof.ETC.measurable_realKernelRegretOfExplorationPrefix theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:158
BanditRLProof.ETC.realKernelRegret_realExplorationArgmaxAction_eq_prefixFunctional theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:184
BanditRLProof.ETC.realKernelRegret_eq_of_action_eq_on_lt theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:196
BanditRLProof.ETC.real_trajMeasure_const_eq_infinitePi theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:208
BanditRLProof.ETC.realExplorationPrefixOfFiniteRewardHistory definition ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:231
BanditRLProof.ETC.measurable_realExplorationPrefixOfFiniteRewardHistory theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:240
BanditRLProof.ETC.realExplorationPrefixOfFiniteRewardHistory_of_trace theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:248
BanditRLProof.ETC.integral_realKernelRegret_realExplorationArgmaxAction_le_exact_sum_of_prefixLaw_eq_infinitePi theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:260
BanditRLProof.ETC.integral_realKernelRegret_externalAction_le_exact_sum_of_prefixLaw_eq_infinitePi theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:364
BanditRLProof.ETC.integral_realKernelRegret_externalAction_le_exact_sum_of_initial_map_eq_condDistrib theorem ETC BanditRLProof.Algorithms.ETCRealPrefixLawTransport Compiled BanditRLProof/Algorithms/ETCRealPrefixLawTransport.lean:426
BanditRLProof.ETC.integral_realKernelRegret_externalAction_le_exact_sum_of_actionDependent_actionRewardHistory_condDistrib theorem ETC BanditRLProof.Algorithms.ETCRealSourceAdapter Compiled BanditRLProof/Algorithms/ETCRealSourceAdapter.lean:27
BanditRLProof.ETC.pseudoRegret_exploreArm_explorationPulls_mul_K_le_sum_gap_mul_explorationPulls theorem ETC BanditRLProof.Algorithms.ETCRegretLemmas Compiled BanditRLProof/Algorithms/ETCRegretLemmas.lean:22
BanditRLProof.ETC.pseudoRegret_actionWithCommit_explorationPulls_mul_K_le_sum_gap_mul_explorationPulls theorem ETC BanditRLProof.Algorithms.ETCRegretLemmas Compiled BanditRLProof/Algorithms/ETCRegretLemmas.lean:48
BanditRLProof.ETC.pseudoRegret_actionWithCommit_explorationPulls_mul_K_add_le_sum_gap_mul_suffix_count_budget theorem ETC BanditRLProof.Algorithms.ETCRegretLemmas Compiled BanditRLProof/Algorithms/ETCRegretLemmas.lean:79
BanditRLProof.ETC.pseudoRegret_actionWithCommit_explorationPulls_mul_K_add_le_sum_gap_mul_explorationPulls_add_suffix theorem ETC BanditRLProof.Algorithms.ETCRegretLemmas Compiled BanditRLProof/Algorithms/ETCRegretLemmas.lean:114
BanditRLProof.ETC.pseudoRegret_actionWithCommit_explorationPulls_mul_K_add_eq_add_suffix_gap theorem ETC BanditRLProof.Algorithms.ETCRegretLemmas Compiled BanditRLProof/Algorithms/ETCRegretLemmas.lean:149
BanditRLProof.ETC.pseudoRegret_actionWithCommit_explorationPulls_mul_K_add_eq_of_commitArm_eq_bestArm theorem ETC BanditRLProof.Algorithms.ETCRegretLemmas Compiled BanditRLProof/Algorithms/ETCRegretLemmas.lean:184
BanditRLProof.ETC.pseudoRegret_actionWithCommit_explorationPulls_mul_K_add_le_sum_gap_mul_explorationPulls_of_commitArm_eq_bestArm theorem ETC BanditRLProof.Algorithms.ETCRegretLemmas Compiled BanditRLProof/Algorithms/ETCRegretLemmas.lean:209
BanditRLProof.ETC.pseudoRegret_actionWithCommit_explorationPulls_mul_K_add_le_sum_gap_mul_explorationPulls_add_suffix_gap theorem ETC BanditRLProof.Algorithms.ETCRegretLemmas Compiled BanditRLProof/Algorithms/ETCRegretLemmas.lean:239
BanditRLProof.ETC.centeredPairwiseRewardDiff definition ETC BanditRLProof.Algorithms.ETCSumRewardsDiff Compiled BanditRLProof/Algorithms/ETCSumRewardsDiff.lean:28
BanditRLProof.ETC.centeredPairwiseGapThreshold definition ETC BanditRLProof.Algorithms.ETCSumRewardsDiff Compiled BanditRLProof/Algorithms/ETCSumRewardsDiff.lean:44
BanditRLProof.ETC.selectedSubMean_sum_eq_sumRewards_sub_pullCount_mul theorem ETC BanditRLProof.Algorithms.ETCSumRewardsDiff Compiled BanditRLProof/Algorithms/ETCSumRewardsDiff.lean:59
BanditRLProof.ETC.meanSubSelected_sum_eq_pullCount_mul_sub_sumRewards theorem ETC BanditRLProof.Algorithms.ETCSumRewardsDiff Compiled BanditRLProof/Algorithms/ETCSumRewardsDiff.lean:106
BanditRLProof.ETC.sumRewards_le_imp_centered_pairwise_sum_ge theorem ETC BanditRLProof.Algorithms.ETCSumRewardsDiff Compiled BanditRLProof/Algorithms/ETCSumRewardsDiff.lean:156
BanditRLProof.ETC.empMeanAtExploration_ge_best_event_subset_centered_pairwise_sum_event theorem ETC BanditRLProof.Algorithms.ETCSumRewardsDiff Compiled BanditRLProof/Algorithms/ETCSumRewardsDiff.lean:200
BanditRLProof.ETC.actionWithCommit definition ETC BanditRLProof.Algorithms.ETCTrace Compiled BanditRLProof/Algorithms/ETCTrace.lean:17
BanditRLProof.ETC.actionWithCommit_eq_exploreArm_of_lt theorem ETC BanditRLProof.Algorithms.ETCTrace Compiled BanditRLProof/Algorithms/ETCTrace.lean:32
BanditRLProof.ETC.actionWithCommit_eq_commitArm_of_ge theorem ETC BanditRLProof.Algorithms.ETCTrace Compiled BanditRLProof/Algorithms/ETCTrace.lean:45
BanditRLProof.ETC.actionWithCommit_eq_bestArm_of_commitArm_eq_bestArm_of_explorationPulls_mul_K_le theorem ETC BanditRLProof.Algorithms.ETCTrace Compiled BanditRLProof/Algorithms/ETCTrace.lean:59
BanditRLProof.ETC.pullCount_actionWithCommit_eq_pullCount_exploreArm_of_le theorem ETC BanditRLProof.Algorithms.ETCTraceCountLemmas Compiled BanditRLProof/Algorithms/ETCTraceCountLemmas.lean:23
BanditRLProof.ETC.pullCount_actionWithCommit_explorationPulls_mul_K_eq theorem ETC BanditRLProof.Algorithms.ETCTraceCountLemmas Compiled BanditRLProof/Algorithms/ETCTraceCountLemmas.lean:53
BanditRLProof.ETC.pullCount_actionWithCommit_explorationPulls_mul_K_pos theorem ETC BanditRLProof.Algorithms.ETCTraceCountLemmas Compiled BanditRLProof/Algorithms/ETCTraceCountLemmas.lean:76
BanditRLProof.ETC.ratCast_pullCount_actionWithCommit_explorationPulls_mul_K_pos theorem ETC BanditRLProof.Algorithms.ETCTraceCountLemmas Compiled BanditRLProof/Algorithms/ETCTraceCountLemmas.lean:96
BanditRLProof.ETC.ratCast_pullCount_actionWithCommit_explorationPulls_mul_K_ne_zero theorem ETC BanditRLProof.Algorithms.ETCTraceCountLemmas Compiled BanditRLProof/Algorithms/ETCTraceCountLemmas.lean:115
BanditRLProof.ETC.pullCount_actionWithCommit_succ_eq_add_if_commitArm_of_ge theorem ETC BanditRLProof.Algorithms.ETCTraceCountLemmas Compiled BanditRLProof/Algorithms/ETCTraceCountLemmas.lean:135
BanditRLProof.ETC.pullCount_actionWithCommit_explorationPulls_mul_K_add_eq theorem ETC BanditRLProof.Algorithms.ETCTraceCountLemmas Compiled BanditRLProof/Algorithms/ETCTraceCountLemmas.lean:155
BanditRLProof.ETC.pullCount_actionWithCommit_explorationPulls_mul_K_add_eq_of_ne theorem ETC BanditRLProof.Algorithms.ETCTraceCountLemmas Compiled BanditRLProof/Algorithms/ETCTraceCountLemmas.lean:193
BanditRLProof.ETC.pullCount_actionWithCommit_explorationPulls_mul_K_add_eq_commitArm theorem ETC BanditRLProof.Algorithms.ETCTraceCountLemmas Compiled BanditRLProof/Algorithms/ETCTraceCountLemmas.lean:210
BanditRLProof.ETC.prob_argmaxCommitOracle_ne_bestArm_le_filtered_sum_centeredDiffSubGaussianTail theorem ETC BanditRLProof.Algorithms.ETCWrongCommitCanonicalTail Compiled BanditRLProof/Algorithms/ETCWrongCommitCanonicalTail.lean:24
BanditRLProof.ETC.pseudoRegret_actionWithCommit_choice_le_sum_gap_mul_explorationPulls_add_suffix_badGap theorem ETC BanditRLProof.Algorithms.ETCWrongCommitRegretAssembly Compiled BanditRLProof/Algorithms/ETCWrongCommitRegretAssembly.lean:26
BanditRLProof.KLUCB.IsBernoulliParameter definition Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:23
BanditRLProof.KLUCB.bernoulliKLCore definition Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:32
BanditRLProof.KLUCB.bernoulliKL definition Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:43
BanditRLProof.KLUCB.bernoulliKL_nonneg theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:55
BanditRLProof.KLUCB.bernoulliKL_eq_top_of_not_left theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:59
BanditRLProof.KLUCB.bernoulliKL_eq_top_of_not_right theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:65
BanditRLProof.KLUCB.bernoulliKL_zero_zero theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:73
BanditRLProof.KLUCB.bernoulliKL_one_one theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:77
BanditRLProof.KLUCB.bernoulliKL_right_zero theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:81
BanditRLProof.KLUCB.bernoulliKL_right_one theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:88
BanditRLProof.KLUCB.bernoulliKL_eq_top_right_zero theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:94
BanditRLProof.KLUCB.bernoulliKL_eq_top_right_one theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:99
BanditRLProof.KLUCB.bernoulliKL_zero_left_of_interior theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:104
BanditRLProof.KLUCB.bernoulliKL_one_left_of_interior theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:116
BanditRLProof.KLUCB.bernoulliKLCore_self theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:129
BanditRLProof.KLUCB.bernoulliKLCore_eq_klFun theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:135
BanditRLProof.KLUCB.bernoulliKLCore_nonneg theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:148
BanditRLProof.KLUCB.bernoulliKL_eq_of_interior theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:163
BanditRLProof.KLUCB.bernoulliKLExpanded definition Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:174
BanditRLProof.KLUCB.bernoulliKLCore_eq_expanded theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:179
BanditRLProof.KLUCB.hasDerivAt_bernoulliKLExpanded_right theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:189
BanditRLProof.KLUCB.half_sq_sub_le_bernoulliKLCore theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:209
BanditRLProof.KLUCB.bernoulliKLCore_le_sq_div theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:305
BanditRLProof.KLUCB.ennnreal_half_sq_sub_le_bernoulliKL theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:356
BanditRLProof.KLUCB.bernoulliKL_le_of_sq_le theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:363
BanditRLProof.KLUCB.bernoulliKL_self theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:373
BanditRLProof.KLUCB.continuousAt_bernoulliKLCore_right theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:387
BanditRLProof.KLUCB.confidenceSet definition Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:408
BanditRLProof.KLUCB.index definition Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:415
BanditRLProof.KLUCB.confidenceSet_bddAbove theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:419
BanditRLProof.KLUCB.mem_confidenceSet_self theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:426
BanditRLProof.KLUCB.mem_confidenceSet_of_natCast_mul_core_le theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:436
BanditRLProof.KLUCB.natCast_mul_half_sq_sub_le_budget_of_mem theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:448
BanditRLProof.KLUCB.confidenceSet_nonempty theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:463
BanditRLProof.KLUCB.index_le_one theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:469
BanditRLProof.KLUCB.index_nonneg theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:477
BanditRLProof.KLUCB.index_mem_Icc theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:486
BanditRLProof.KLUCB.mem_confidenceSet_zero_iff theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:494
BanditRLProof.KLUCB.index_zero_count theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:499
BanditRLProof.KLUCB.le_index_of_mem_confidenceSet theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:511
BanditRLProof.KLUCB.exists_mem_confidenceSet_of_lt_index theorem Foundations BanditRLProof.Algorithms.KLUCBBernoulli Compiled BanditRLProof/Algorithms/KLUCBBernoulli.lean:520
BanditRLProof.KLUCB.generatedBudgetAt definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:24
BanditRLProof.KLUCB.generatedBudgetAt_nonneg theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:34
BanditRLProof.KLUCB.generatedIndexAt definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:46
BanditRLProof.KLUCB.historyIndex definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:59
BanditRLProof.KLUCB.measurable_historyIndex theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:79
BanditRLProof.KLUCB.historyNextArm definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:87
BanditRLProof.KLUCB.historyIndex_le_nextArm_of_K_le theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:95
BanditRLProof.KLUCB.pairHistory definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:108
BanditRLProof.KLUCB.historyState definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:126
BanditRLProof.KLUCB.measurable_historyState theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:133
BanditRLProof.KLUCB.historyPolicy definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:140
BanditRLProof.KLUCB.generatedAction definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:150
BanditRLProof.KLUCB.generatedAction_succ theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:160
BanditRLProof.KLUCB.pairHistory_eq_finitePairHistoryOfTrace theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:172
BanditRLProof.KLUCB.historyIndex_finitePairHistoryOfTrace theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:214
BanditRLProof.KLUCB.generatedIndexAt_le_selected_of_K_le theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:232
BanditRLProof.KLUCB.generatedAction_succ_eq_initializationArm_of_lt theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:266
BanditRLProof.KLUCB.successorArmPullCount_generatedAction_K_add_one_eq_one theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:275
BanditRLProof.KLUCB.successorArmPullCount_generatedAction_pos_of_K_le theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:298
BanditRLProof.KLUCB.K_le_of_generatedAction_selected_and_count_pos theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:317
BanditRLProof.KLUCB.armMean_mem_confidenceSet_of_abs_lt_radius theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:347
BanditRLProof.KLUCB.armMean_le_generatedIndexAt_of_abs_lt_radius theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:413
BanditRLProof.KLUCB.margin_mul_gap_div_eight_le_radius_of_selected_of_not_badEvent theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:438
BanditRLProof.KLUCB.pullThreshold definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:610
BanditRLProof.KLUCB.pullCount_le_of_not_badEvent theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:616
BanditRLProof.KLUCB.actionRewardHistoryStepKernelFamily_allTimeConfidence theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:708
BanditRLProof.KLUCB.generatedKLAllTimeBadEvent definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:839
BanditRLProof.KLUCB.generatedKLAllTimeBadEvent_subset_absBadEvent theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:855
BanditRLProof.KLUCB.measure_generatedKLAllTimeBadEvent_le theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:890
BanditRLProof.KLUCB.sumRewards_nonneg_of_mem_Icc_zero_one theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:932
BanditRLProof.KLUCB.sumRewards_le_pullCount_of_mem_Icc_zero_one theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:947
BanditRLProof.KLUCB.successorArmEmpiricalMean_isBernoulliParameter_of_rewards_mem_Icc theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:966
BanditRLProof.KLUCB.generatedEmpiricalMean_isBernoulliParameter_of_rewards_mem_Icc theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:998
BanditRLProof.KLUCB.successorArmEmpiricalMean_isBernoulliParameter_of_rewards_mem_Icc' theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1013
BanditRLProof.KLUCB.generatedEmpiricalMean_isBernoulliParameter_of_rewards_mem_Icc' theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1027
BanditRLProof.KLUCB.measure_pullCount_gt_threshold_le_of_allTimeConfidence theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1040
BanditRLProof.KLUCB.lintegral_pullCount_le_of_allTimeConfidence theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1075
BanditRLProof.KLUCB.generatedRegretAction definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1132
BanditRLProof.KLUCB.measurable_generatedRegretAction theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1139
BanditRLProof.KLUCB.pullCount_generatedRegretAction_eq theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1153
BanditRLProof.KLUCB.lintegral_ofReal_pseudoRegret_generatedKLUCBBounded_le theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1169
BanditRLProof.KLUCB.allHorizonPullCount_of_not_badEvent theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1228
BanditRLProof.KLUCB.actionRewardTrajMeasure definition Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1258
BanditRLProof.KLUCB.measure_allTimeBadEvent_le_trajMeasure theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1287
BanditRLProof.KLUCB.measure_generatedKLAllTimeBadEvent_le_trajMeasure theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1321
BanditRLProof.KLUCB.lintegral_ofReal_pseudoRegret_generatedKLUCBBounded_le_trajMeasure theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1380
BanditRLProof.KLUCB.measurable_generatedAction theorem Foundations BanditRLProof.Algorithms.KLUCBGeneratedRegret Compiled BanditRLProof/Algorithms/KLUCBGeneratedRegret.lean:1442
BanditRLProof.Thompson.PriorSketch structure Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:17
BanditRLProof.Thompson.obligationNames definition Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:24
BanditRLProof.Thompson.PosteriorActionIdentityLedger structure Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:49
BanditRLProof.Thompson.bestAction_measurable_of_countable_env theorem Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:71
BanditRLProof.Thompson.PosteriorActionIdentityLedger.ofCountableEnv definition Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:93
BanditRLProof.Thompson.PosteriorActionIdentityLedger.ofPosteriorMap definition Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:116
BanditRLProof.Thompson.PosteriorActionIdentityLedger.actionKernel_eq_posterior_map theorem Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:131
BanditRLProof.Thompson.PosteriorActionIdentityLedger.actionKernel_apply_eq_posteriorBest_map theorem Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:141
BanditRLProof.Thompson.PosteriorActionIdentityLedger.actionKernel_apply_singleton_eq_posteriorBest_preimage theorem Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:155
BanditRLProof.Thompson.BayesianPosteriorActionSource structure Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:177
BanditRLProof.Thompson.condDistrib_action_ae_eq_bestAction_of_bayesianPosteriorActionSource theorem Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:204
BanditRLProof.Thompson.condDistrib_action_ae_eq_bestAction_of_posteriorMap theorem Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:241
BanditRLProof.Thompson.condDistrib_action_ae_eq_bestAction_of_bayesianPairMap theorem Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:283
BanditRLProof.Thompson.condDistrib_action_ae_eq_bestAction_of_canonicalPriorLikelihood theorem Thompson sampling BanditRLProof.Algorithms.Thompson Compiled BanditRLProof/Algorithms/Thompson.lean:321
BanditRLProof.Thompson.compProd_withDensity_left theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:26
BanditRLProof.Thompson.comp_withDensity_history theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:66
BanditRLProof.Thompson.map_swap_withDensity_snd theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:93
BanditRLProof.Thompson.compProd_eq_compProd_withDensity_snd_of_ae_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:112
BanditRLProof.Thompson.AlgorithmDensityPosteriorSource structure Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:164
BanditRLProof.Thompson.algorithmDensityPosteriorSource_of_condDistrib_history_withDensity definition Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:190
BanditRLProof.Thompson.referencePosterior_ae_eq_condDistrib_of_algorithmDensitySource theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:296
BanditRLProof.Thompson.referencePolicySampler_condDistrib_action_ae_eq_bestAction_of_algorithmDensitySource theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:357
BanditRLProof.Thompson.referencePolicySampler_condDistrib_action_ae_eq_bestAction_of_condDistrib_history_withDensity theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:396
BanditRLProof.Thompson.finitePairReferencePolicySampler_condDistrib_action_ae_eq_bestAction_of_algorithmDensitySource theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:442
BanditRLProof.Thompson.finitePairReferencePolicySampler_condDistrib_action_ae_eq_bestAction_of_condDistrib_history_withDensity theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensity Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensity.lean:511
BanditRLProof.Thompson.HistoryAlgorithm structure Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:25
BanditRLProof.Thompson.HistoryEnvironment structure Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:49
BanditRLProof.Thompson.historyStepKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:75
BanditRLProof.Thompson.HistoryAlgorithmAbsolutelyContinuous structure Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:95
BanditRLProof.Thompson.singletonPairHistory definition Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:104
BanditRLProof.Thompson.pairHistoryPrefix definition Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:110
BanditRLProof.Thompson.pairHistoryLast definition Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:118
BanditRLProof.Thompson.measurable_singletonPairHistory theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:124
BanditRLProof.Thompson.measurable_pairHistoryPrefix theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:130
BanditRLProof.Thompson.measurable_pairHistoryLast theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:136
BanditRLProof.Thompson.pairHistoryPrefix_extendPairHistorySucc theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:143
BanditRLProof.Thompson.pairHistoryLast_extendPairHistorySucc theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:153
BanditRLProof.Thompson.historyDensity definition Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:161
BanditRLProof.Thompson.measurable_historyDensity theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:175
BanditRLProof.Thompson.map_withDensity_comp theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:192
BanditRLProof.Thompson.compProd_withDensity_withDensity theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:207
BanditRLProof.Thompson.kernel_withDensity_rnDeriv_eq_of_absolutelyContinuous theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:228
BanditRLProof.Thompson.kernel_compProd_withDensity_left theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:243
BanditRLProof.Thompson.historyStepKernel_eq_withDensity theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:273
BanditRLProof.Thompson.IsHistoryAlgorithmEnvironmentSequence structure Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:312
BanditRLProof.Thompson.isHistoryAlgorithmEnvironmentSequence_of_split definition Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:337
BanditRLProof.Thompson.nextPairJointLaw_eq_compProd theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:396
BanditRLProof.Thompson.finitePairHistory_map_eq_withDensity theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:433
BanditRLProof.Thompson.ConditionalHistoryAlgorithmDensitySource structure Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:732
BanditRLProof.Thompson.condDistrib_finitePairHistory_eq_withDensity_of_conditionalProcessSource theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:776
BanditRLProof.Thompson.finitePairReferencePolicySampler_condDistrib_action_ae_eq_bestAction_of_conditionalProcessSource theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:873
BanditRLProof.Thompson.ConditionalHistoryAlgorithmEnvironmentSplitSource structure Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:935
BanditRLProof.Thompson.ConditionalHistoryAlgorithmDensitySplitSource structure Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:989
BanditRLProof.Thompson.conditionalHistoryAlgorithmDensitySource_of_split definition Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:1021
BanditRLProof.Thompson.condDistrib_finitePairHistory_eq_withDensity_of_conditionalSplitSource theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:1141
BanditRLProof.Thompson.finitePairReferencePolicySampler_condDistrib_action_ae_eq_bestAction_of_conditionalSplitSource theorem Thompson sampling BanditRLProof.Algorithms.ThompsonAlgorithmDensityProcess Compiled BanditRLProof/Algorithms/ThompsonAlgorithmDensityProcess.lean:1187
BanditRLProof.Thompson.HistoryActionScore structure Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:23
BanditRLProof.Thompson.HistoryActionScore.atTrace definition Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:37
BanditRLProof.Thompson.HistoryActionScore.atBestTrace definition Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:48
BanditRLProof.Thompson.HistoryActionScore.measurable_atTrace theorem Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:59
BanditRLProof.Thompson.HistoryActionScore.measurable_atBestTrace theorem Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:77
BanditRLProof.Thompson.integral_comp_eq_of_map_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:100
BanditRLProof.Thompson.integral_historyAction_eq_of_condDistrib_ae_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:121
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryKernel_map_action_zero theorem Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:146
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryMeasure_map_action_zero theorem Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:168
BanditRLProof.Thompson.uniformReferenceThompsonAlgorithm_map_action_zero_eq_bestAction theorem Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:201
BanditRLProof.Thompson.trajectoryHistoryScore definition Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:245
BanditRLProof.Thompson.trajectoryBestHistoryScore definition Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:254
BanditRLProof.Thompson.uniformReferenceThompsonAlgorithm_integral_historyScore_eq_bestAction theorem Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:268
BanditRLProof.Thompson.IsOptimalMeanSelector definition Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:341
BanditRLProof.Thompson.trajectoryBayesMeanRegret definition Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:349
BanditRLProof.Thompson.integral_trajectoryBayesMeanRegret_eq_add_historyScore theorem Thompson sampling BanditRLProof.Algorithms.ThompsonBayesRegretDecomposition Compiled BanditRLProof/Algorithms/ThompsonBayesRegretDecomposition.lean:362
BanditRLProof.Thompson.canonicalActionKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:23
BanditRLProof.Thompson.canonicalActionKernelOnPair definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:50
BanditRLProof.Thompson.canonicalSamplerMeasure definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:83
BanditRLProof.Thompson.canonicalSamplerEnv definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:111
BanditRLProof.Thompson.canonicalSamplerHistory definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:116
BanditRLProof.Thompson.canonicalSamplerAction definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:121
BanditRLProof.Thompson.canonicalSamplerEnv_measurable theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:125
BanditRLProof.Thompson.canonicalSamplerHistory_measurable theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:131
BanditRLProof.Thompson.canonicalSamplerAction_measurable theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:137
BanditRLProof.Thompson.map_compProd_comap_snd theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:147
BanditRLProof.Thompson.canonicalSampler_env_history_map_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:181
BanditRLProof.Thompson.canonicalSampler_history_action_map_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:200
BanditRLProof.Thompson.canonicalSampler_condDistrib_action_ae_eq_actionKernel theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:242
BanditRLProof.Thompson.canonicalSampler_condDistrib_action_ae_eq_bestAction theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalSampler Compiled BanditRLProof/Algorithms/ThompsonCanonicalSampler.lean:271
BanditRLProof.Thompson.canonicalHistoryTrajectoryMeasure definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:21
BanditRLProof.Thompson.canonicalHistoryTrajectoryAction definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:42
BanditRLProof.Thompson.canonicalHistoryTrajectoryReward definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:48
BanditRLProof.Thompson.measurable_canonicalHistoryTrajectoryAction_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:53
BanditRLProof.Thompson.measurable_canonicalHistoryTrajectoryReward_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:60
BanditRLProof.Thompson.canonicalHistoryTrajectory_initialPair_map_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:67
BanditRLProof.Thompson.canonicalHistoryTrajectory_step_condDistrib theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:92
BanditRLProof.Thompson.canonicalHistoryAlgorithmEnvironmentSequence definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:136
BanditRLProof.Thompson.initialAction_map_eq_of_historyAlgorithmEnvironmentSequence theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:154
BanditRLProof.Thompson.initialFeedback_condDistrib_of_historyAlgorithmEnvironmentSequence theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:180
BanditRLProof.Thompson.historyStepKernel_map_fst theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:202
BanditRLProof.Thompson.policy_condDistrib_of_historyAlgorithmEnvironmentSequence theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:213
BanditRLProof.Thompson.feedback_condDistrib_of_historyAlgorithmEnvironmentSequence theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:262
BanditRLProof.Thompson.HistoryAlgorithmEnvironmentSplitSource structure Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:339
BanditRLProof.Thompson.HistoryAlgorithmEnvironmentSplitSource.toSequence definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:374
BanditRLProof.Thompson.canonicalHistoryAlgorithmEnvironmentSplitSource definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:395
BanditRLProof.Thompson.canonicalHistoryAlgorithmEnvironmentSequence_of_split definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:433
BanditRLProof.Thompson.kernelWithInput definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:449
BanditRLProof.Thompson.kernelWithInput_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:466
BanditRLProof.Thompson.condDistrib_id_fst_compProd_ae_eq_kernelWithInput theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:487
BanditRLProof.Thompson.environmentTrajectoryAction definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:531
BanditRLProof.Thompson.environmentTrajectoryReward definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:537
BanditRLProof.Thompson.measurable_environmentTrajectoryAction_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:542
BanditRLProof.Thompson.measurable_environmentTrajectoryReward_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:550
BanditRLProof.Thompson.historyAlgorithmEnvironmentSequence_of_measure_eq definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:559
BanditRLProof.Thompson.mappedCanonicalHistoryAlgorithmEnvironmentSequence definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:578
BanditRLProof.Thompson.kernelWithInputHistoryAlgorithmEnvironmentSequence definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:686
BanditRLProof.Thompson.conditionalHistoryAlgorithmEnvironmentSequence_of_canonicalTrajectoryKernel theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:722
BanditRLProof.Thompson.conditionalHistoryAlgorithmEnvironmentSplitSource_of_canonicalTrajectoryKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:764
BanditRLProof.Thompson.conditionalHistoryAlgorithmDensitySplitSource_of_canonicalTrajectoryKernels definition Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:831
BanditRLProof.Thompson.finitePairReferencePolicySampler_condDistrib_action_ae_eq_bestAction_of_canonicalTrajectoryKernels theorem Thompson sampling BanditRLProof.Algorithms.ThompsonCanonicalTrajectory Compiled BanditRLProof/Algorithms/ThompsonCanonicalTrajectory.lean:878
BanditRLProof.Thompson.clippedUCB definition Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:24
BanditRLProof.Thompson.clippedUCBHistory definition Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:37
BanditRLProof.Thompson.clippedUCB_zero theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:50
BanditRLProof.Thompson.clippedUCB_mem_Icc theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:57
BanditRLProof.Thompson.finset_sum_sqrt_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:68
BanditRLProof.Thompson.finset_sum_one_div_sqrt_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:77
BanditRLProof.Thompson.sum_clippedUCB_action_sub_mean_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:106
BanditRLProof.Thompson.clippedUCBHistory_mem_Icc theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:237
BanditRLProof.Thompson.measurable_clippedUCBHistory theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:249
BanditRLProof.Thompson.measurable_uncurry_clippedUCBHistory theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:275
BanditRLProof.Thompson.clippedUCBHistoryScore definition Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:285
BanditRLProof.Thompson.clippedUCBHistory_finitePairHistoryOfTrace theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:296
BanditRLProof.Thompson.clippedUCBHistoryScore_atTrace theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:308
BanditRLProof.Thompson.clippedUCBHistoryScore_atBestTrace theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:320
BanditRLProof.Thompson.integrable_of_measurable_mem_Icc theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:334
BanditRLProof.Thompson.integrable_trajectoryHistoryScore_clippedUCB theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:347
BanditRLProof.Thompson.integrable_trajectoryBestHistoryScore_clippedUCB theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:368
BanditRLProof.Thompson.integrable_trajectoryMean_bestAction theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:391
BanditRLProof.Thompson.integrable_trajectoryMean_action theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:407
BanditRLProof.Thompson.integral_trajectoryBayesMeanRegret_eq_add_clippedUCB theorem Thompson sampling BanditRLProof.Algorithms.ThompsonClippedUCBScore Compiled BanditRLProof/Algorithms/ThompsonClippedUCBScore.lean:428
BanditRLProof.Thompson.MeasurableHistoryEnvironment structure Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:25
BanditRLProof.Thompson.MeasurableHistoryEnvironment.at definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:52
BanditRLProof.Thompson.measurableEnvironmentInitialPairKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:63
BanditRLProof.Thompson.measurableEnvironmentHistoryStepKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:83
BanditRLProof.Thompson.measurableEnvironmentInitialPairKernel_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:104
BanditRLProof.Thompson.measurableEnvironmentHistoryStepKernel_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:117
BanditRLProof.Thompson.measurableTrajectoryPrefixEnvironment definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:133
BanditRLProof.Thompson.measurableTrajectoryPrefixHistory definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:139
BanditRLProof.Thompson.measurable_measurableTrajectoryPrefixEnvironment theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:148
BanditRLProof.Thompson.measurable_measurableTrajectoryPrefixHistory theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:158
BanditRLProof.Thompson.measurable_measurableTrajectoryPrefixEnvironmentHistory theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:170
BanditRLProof.Thompson.retainEnvironmentKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:185
BanditRLProof.Thompson.retainEnvironmentKernel_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:206
BanditRLProof.Thompson.retainEnvironmentKernel_map_snd theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:230
BanditRLProof.Thompson.canonicalMeasurableEnvironmentStepKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:249
BanditRLProof.Thompson.canonicalMeasurableEnvironmentStepKernel_succ_apply_map_snd theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:287
BanditRLProof.Thompson.measurableEnvironmentInitialStatePrefix definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:312
BanditRLProof.Thompson.measurable_measurableEnvironmentInitialStatePrefix theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:318
BanditRLProof.Thompson.measurableEnvironmentPairTrace definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:329
BanditRLProof.Thompson.measurable_measurableEnvironmentPairTrace theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:335
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:348
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryKernel_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:373
BanditRLProof.Thompson.measurableTrajectoryPrefixEnvironment_initialStatePrefix theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:390
BanditRLProof.Thompson.measurableTrajectoryPrefixEnvironment_ae_eq_of_traj theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:399
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryKernel_map_eval_zero theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:460
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryKernel_map_prefix_next_eq_compProd theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:533
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryKernel_condDistrib_succ theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:660
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryKernel_apply_eq_canonical_of_step_condDistrib theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:687
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryKernel_apply_eq_canonical theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:734
BanditRLProof.Thompson.finitePairReferencePolicySampler_condDistrib_action_ae_eq_bestAction_of_measurableEnvironment_stepCondDistrib theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:754
BanditRLProof.Thompson.finitePairReferencePolicySampler_condDistrib_action_ae_eq_bestAction_of_measurableEnvironment theorem Thompson sampling BanditRLProof.Algorithms.ThompsonMeasurableTrajectory Compiled BanditRLProof/Algorithms/ThompsonMeasurableTrajectory.lean:832
BanditRLProof.Thompson.uniformActionMeasure definition Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:22
BanditRLProof.Thompson.absolutelyContinuous_uniformActionMeasure theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:35
BanditRLProof.Thompson.uniformHistoryAlgorithm definition Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:57
BanditRLProof.Thompson.historyAlgorithmAbsolutelyContinuous_uniform theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:67
BanditRLProof.Thompson.trajectoryMixture_map_history_action_eq_compProd theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:85
BanditRLProof.Thompson.trajectoryMixture_condDistrib_action theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:148
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryKernel_map_history_action_eq_compProd theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:172
BanditRLProof.Thompson.canonicalMeasurableEnvironmentTrajectoryMeasure_condDistrib_action theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:209
BanditRLProof.Thompson.finitePairReferencePosterior_ae_eq_condDistrib_of_conditionalProcessSource theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:241
BanditRLProof.Thompson.referencePosteriorHistoryAlgorithm definition Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:305
BanditRLProof.Thompson.referencePosteriorHistoryAlgorithm_initialAction theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:334
BanditRLProof.Thompson.referencePosteriorHistoryAlgorithm_policy theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:347
BanditRLProof.Thompson.referencePosteriorHistoryAlgorithm_trajectory_condDistrib_action_ae_eq_bestAction theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:383
BanditRLProof.Thompson.uniformReferenceThompsonAlgorithm definition Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:490
BanditRLProof.Thompson.uniformReferenceThompsonAlgorithm_trajectory_condDistrib_action_ae_eq_bestAction theorem Thompson sampling BanditRLProof.Algorithms.ThompsonRecursiveSampler Compiled BanditRLProof/Algorithms/ThompsonRecursiveSampler.lean:507
BanditRLProof.Thompson.referencePosterior definition Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:27
BanditRLProof.Thompson.referencePosterior_kernel theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:42
BanditRLProof.Thompson.referenceActionKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:57
BanditRLProof.Thompson.policySamplerMeasure definition Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:90
BanditRLProof.Thompson.policySamplerEnv definition Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:112
BanditRLProof.Thompson.policySamplerHistory definition Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:118
BanditRLProof.Thompson.policySamplerAction definition Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:124
BanditRLProof.Thompson.policySamplerEnv_measurable theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:127
BanditRLProof.Thompson.policySamplerHistory_measurable theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:134
BanditRLProof.Thompson.policySamplerAction_measurable theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:141
BanditRLProof.Thompson.map_compProd_comap_history theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:153
BanditRLProof.Thompson.policySampler_base_map_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:183
BanditRLProof.Thompson.policySampler_history_action_map_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:207
BanditRLProof.Thompson.policySampler_condDistrib_action_ae_eq_policy theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:229
BanditRLProof.Thompson.policySampler_condDistrib_env_ae_eq_of_base theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:251
BanditRLProof.Thompson.referencePolicySampler_condDistrib_action_ae_eq_bestAction_of_posterior_invariance theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:307
BanditRLProof.Thompson.finitePairReferencePolicySampler_condDistrib_action_ae_eq_bestAction_of_posterior_invariance theorem Thompson sampling BanditRLProof.Algorithms.ThompsonReferencePolicy Compiled BanditRLProof/Algorithms/ThompsonReferencePolicy.lean:373
BanditRLProof.Thompson.UnitArmStream abbreviation Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:23
BanditRLProof.Thompson.uniformUnitArmStreamMeasure definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:27
BanditRLProof.Thompson.stationaryRewardSampler definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:38
BanditRLProof.Thompson.measurable_uncurry_stationaryRewardSampler theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:44
BanditRLProof.Thompson.stationaryRewardSampler_map_volume theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:50
BanditRLProof.Thompson.rewardStreamOfUnitArmStream definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:59
BanditRLProof.Thompson.measurable_rewardStreamOfUnitArmStream theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:66
BanditRLProof.Thompson.stationaryRewardKernelAt definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:77
BanditRLProof.Thompson.stationaryRewardKernelAt_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:91
BanditRLProof.Thompson.stationaryArmStreamKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:99
BanditRLProof.Thompson.stationaryArmStreamKernel_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:115
BanditRLProof.Thompson.stationaryMeasurableHistoryEnvironment definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:176
BanditRLProof.Thompson.stationaryMeasurableHistoryEnvironment_initialFeedback theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:185
BanditRLProof.Thompson.stationaryMeasurableHistoryEnvironment_feedback_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:192
BanditRLProof.Thompson.stationaryMeasurableHistoryEnvironment_at_initialFeedback_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:203
BanditRLProof.Thompson.stationaryMeasurableHistoryEnvironment_at_feedback_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:213
BanditRLProof.Thompson.latentArmStreamInitialReward definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:225
BanditRLProof.Thompson.measurable_latentArmStreamInitialReward theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:230
BanditRLProof.Thompson.latentArmStreamNextReward definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:238
BanditRLProof.Thompson.measurable_latentArmStreamNextReward theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:245
BanditRLProof.Thompson.latentArmStreamMeasurableHistoryEnvironment definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:267
BanditRLProof.Thompson.latentArmStreamMeasurableHistoryEnvironment_initialFeedback_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:277
BanditRLProof.Thompson.latentArmStreamMeasurableHistoryEnvironment_feedback_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:286
BanditRLProof.Thompson.measurable_latentArmStreamNextReward_fixed theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:296
BanditRLProof.Thompson.latentArmStreamMeasurableHistoryEnvironment_at_initialFeedback_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:311
BanditRLProof.Thompson.latentArmStreamMeasurableHistoryEnvironment_at_feedback_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:321
BanditRLProof.Thompson.canonicalLatentArmStreamTrajectory_reward_zero_ae theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:332
BanditRLProof.Thompson.canonicalLatentArmStreamTrajectory_reward_succ_ae theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:376
BanditRLProof.Thompson.canonicalLatentArmStreamTrajectory_reward_eq_rewardFromArmStream_ae theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:455
BanditRLProof.UCB.measurable_rewardFromArmStream_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:493
BanditRLProof.UCB.measure_sumRewards_sub_pullCount_mul_ge_le_of_armStream_identDistrib theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:524
BanditRLProof.UCB.measure_pullCount_mul_sub_sumRewards_ge_le_of_armStream_identDistrib theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:583
BanditRLProof.UCB.measure_pos_and_sumRewards_sub_pullCount_mul_ge_le_of_armStream_identDistrib theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:642
BanditRLProof.UCB.measure_pos_and_pullCount_mul_sub_sumRewards_ge_le_of_armStream_identDistrib theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:715
BanditRLProof.UCB.measure_sumRewards_sub_pullCount_mul_ge_le_of_canonicalArmStream theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:790
BanditRLProof.UCB.measure_pullCount_mul_sub_sumRewards_ge_le_of_canonicalArmStream theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:838
BanditRLProof.Thompson.latentArmStreamTrajectoryKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:887
BanditRLProof.Thompson.latentArmStreamTrajectoryMeasure definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:903
BanditRLProof.Thompson.latentArmStreamTrajectoryAction definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:919
BanditRLProof.Thompson.latentArmStreamTrajectoryReward definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:926
BanditRLProof.Thompson.measurable_latentArmStreamTrajectoryAction_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:932
BanditRLProof.Thompson.measurable_latentArmStreamTrajectoryReward_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:939
BanditRLProof.Thompson.measurable_pullCount_selectedArm theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:947
BanditRLProof.Thompson.measurable_sumRewards_selectedArm theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:964
BanditRLProof.Thompson.measurable_realEmpiricalMean_selectedArm theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:984
BanditRLProof.Thompson.identDistrib_fst_latentArmStreamTrajectoryMeasure theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:999
BanditRLProof.Thompson.latentArmStreamTrajectoryReward_eq_rewardFromArmStream_ae theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1015
BanditRLProof.Thompson.measure_latentArmStreamTrajectory_sumRewards_sub_pullCount_mul_ge_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1055
BanditRLProof.Thompson.measure_latentArmStreamTrajectory_pullCount_mul_sub_sumRewards_ge_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1119
BanditRLProof.Thompson.measure_latentArmStreamTrajectory_pos_and_sumRewards_sub_pullCount_mul_ge_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1183
BanditRLProof.Thompson.measure_latentArmStreamTrajectory_pos_and_pullCount_mul_sub_sumRewards_ge_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1249
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryKernel definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1318
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryKernel_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1340
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryKernel_sumRewards_upper_tail theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1355
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryKernel_sumRewards_lower_tail theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1388
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryKernel_pos_and_sumRewards_upper_tail theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1421
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryKernel_pos_and_sumRewards_lower_tail theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1455
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryEnvironment definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1489
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryAction definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1495
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryReward definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1502
BanditRLProof.Thompson.measurable_stationaryLatentArmStreamTrajectoryEnvironment theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1508
BanditRLProof.Thompson.measurable_stationaryLatentArmStreamTrajectoryAction_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1514
BanditRLProof.Thompson.measurable_stationaryLatentArmStreamTrajectoryReward_apply theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1521
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1529
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_sumRewards_upper_tail theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1553
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_sumRewards_lower_tail theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1646
BanditRLProof.Thompson.measure_compProd_le_of_forall_kernel_apply_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1738
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_pos_and_sumRewards_upper_tail theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1754
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_pos_and_sumRewards_lower_tail theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1834
BanditRLProof.Thompson.clippedCountWidthThreshold definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1913
BanditRLProof.Thompson.clippedCountWidthThreshold_nonneg theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1919
BanditRLProof.Thompson.clippedCountWidthThreshold_sq_div_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1925
BanditRLProof.Thompson.sum_clippedCountWidthThreshold_tail_eq theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1948
BanditRLProof.Thompson.measure_biUnion_clippedCountWidthThreshold_le_mul_sub_armPrefixSum_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:1976
BanditRLProof.Thompson.clippedCountWidthThreshold_le_mul_mean_sub_sumRewards theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2015
BanditRLProof.Thompson.clippedCountWidthThreshold_le_sumRewards_sub_mul_mean theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2044
BanditRLProof.Thompson.measure_latentArmStreamTrajectory_exists_realEmpiricalMean_add_width_le_mean_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2078
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_exists_selectedArm_realEmpiricalMean_add_width_le_mean_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2180
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_realEmpiricalMean_add_width_le_mean theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2301
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_mean_le_realEmpiricalMean_sub_width theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2379
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_realEmpiricalMean_add_width_le_mean_le_nat_mul_delta theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2457
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_mean_le_realEmpiricalMean_sub_width_le_nat_mul_delta theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2502
BanditRLProof.Thompson.stationaryLatentArmStreamPrior definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2547
BanditRLProof.Thompson.stationaryLatentArmStreamCanonicalTrajectoryMeasure definition Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2567
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_map_prodAssoc_symm theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2591
BanditRLProof.Thompson.stationaryLatentArmStreamCanonicalTrajectoryMeasure_realEmpiricalMean_add_width_le_mean_le_nat_mul_delta theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2611
BanditRLProof.Thompson.stationaryLatentArmStreamCanonicalTrajectoryMeasure_mean_le_realEmpiricalMean_sub_width_le_nat_mul_delta theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2691
BanditRLProof.Thompson.stationaryLatentArmStreamCanonicalTrajectoryMeasure_exists_selectedArm_realEmpiricalMean_add_width_le_mean_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2771
BanditRLProof.Thompson.stationaryLatentArmStreamCanonicalTrajectoryMeasure_integral_sum_mean_bestAction_sub_clippedUCB_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:2892
BanditRLProof.Thompson.measure_biUnion_clippedCountWidthThreshold_le_armPrefixSum_sub_mul_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:3093
BanditRLProof.Thompson.measure_latentArmStreamTrajectory_exists_mean_le_realEmpiricalMean_sub_width_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:3136
BanditRLProof.Thompson.measure_latentArmStreamTrajectory_exists_arm_exists_mean_le_realEmpiricalMean_sub_width_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:3236
BanditRLProof.Thompson.stationaryLatentArmStreamTrajectoryMeasure_exists_arm_exists_mean_le_realEmpiricalMean_sub_width_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:3299
BanditRLProof.Thompson.stationaryLatentArmStreamCanonicalTrajectoryMeasure_exists_arm_exists_mean_le_realEmpiricalMean_sub_width_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:3406
BanditRLProof.Thompson.stationaryLatentArmStreamCanonicalTrajectoryMeasure_integral_sum_clippedUCB_action_sub_mean_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:3512
BanditRLProof.Thompson.stationaryLatentArmStreamCanonicalTrajectoryMeasure_integral_trajectoryBayesMeanRegret_le_of_delta theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:3723
BanditRLProof.Thompson.stationaryLatentArmStreamCanonicalTrajectoryMeasure_integral_trajectoryBayesMeanRegret_le theorem Thompson sampling BanditRLProof.Algorithms.ThompsonStationaryReward Compiled BanditRLProof/Algorithms/ThompsonStationaryReward.lean:3848
BanditRLProof.UCB.Spec structure UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:28
BanditRLProof.UCB.IndexState structure UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:33
BanditRLProof.UCB.score definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:43
BanditRLProof.UCB.score_eq_empiricalMean theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:46
BanditRLProof.UCB.confidenceScore definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:51
BanditRLProof.UCB.confidenceScore_apply theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:55
BanditRLProof.UCB.score_le_foldl_select theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:60
BanditRLProof.UCB.scoreArgmax definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:121
BanditRLProof.UCB.scoreArgmax_spec theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:129
BanditRLProof.UCB.confidenceScoreArgmaxAction definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:141
BanditRLProof.UCB.confidenceScoreArgmaxAction_score_max theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:154
BanditRLProof.UCB.confidenceScoreArgmaxAction_score_max_of_selected theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:172
BanditRLProof.UCB.meanGap definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:187
BanditRLProof.UCB.meanGap_apply theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:190
BanditRLProof.UCB.meanGap_le_two_radius_of_confidenceScore_max theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:200
BanditRLProof.UCB.not_two_radius_lt_meanGap_of_confidenceScore_max theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:219
BanditRLProof.UCB.upperConfidenceBad definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:236
BanditRLProof.UCB.lowerConfidenceBad definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:242
BanditRLProof.UCB.measurableSet_upperConfidenceBad theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:248
BanditRLProof.UCB.measurableSet_lowerConfidenceBad theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:258
BanditRLProof.UCB.confidenceBadEvent definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:268
BanditRLProof.UCB.measurableSet_confidenceBadEvent theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:275
BanditRLProof.UCB.not_upperConfidenceBad_of_not_confidenceBadEvent theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:289
BanditRLProof.UCB.not_lowerConfidenceBad_of_not_confidenceBadEvent theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:300
BanditRLProof.UCB.meanGap_le_two_radius_of_not_confidenceBadEvent theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:316
BanditRLProof.UCB.measure_confidenceBadEvent_le_sum_upper_lower theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:347
BanditRLProof.UCB.confidenceBadEventAt definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:379
BanditRLProof.UCB.measurableSet_confidenceBadEventAt theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:390
BanditRLProof.UCB.finiteHorizonConfidenceBadEvent definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:403
BanditRLProof.UCB.not_confidenceBadEventAt_of_not_finiteHorizonConfidenceBadEvent theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:414
BanditRLProof.UCB.meanGap_le_two_radius_of_not_finiteHorizonConfidenceBadEvent theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:435
BanditRLProof.UCB.mem_finiteHorizonConfidenceBadEvent_of_two_radius_lt_meanGap_of_score_max theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:462
BanditRLProof.UCB.scoreMaxEvent_subset_finiteHorizonConfidenceBadEvent_of_two_radius_lt_meanGap theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:487
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_sum_upper_lower theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:512
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_tail_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:565
BanditRLProof.UCB.upperConfidenceBad_subset_absDeviation theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:598
BanditRLProof.UCB.lowerConfidenceBad_subset_absDeviation theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:620
BanditRLProof.UCB.measure_upperConfidenceBad_le_absDeviation theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:634
BanditRLProof.UCB.measure_lowerConfidenceBad_le_absDeviation theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:646
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_absDeviation_tail_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:664
BanditRLProof.UCB.chebyshevAbsDeviationTail definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:698
BanditRLProof.UCB.measure_absDeviation_le_chebyshev_tail theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:712
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_chebyshev_tail_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:743
BanditRLProof.UCB.subGaussianOneSidedDeviationTail definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:780
BanditRLProof.UCB.subGaussianOneSidedDeviationTail_le_exp_neg_budget theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:795
BanditRLProof.UCB.subGaussianBudgetRadius definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:825
BanditRLProof.UCB.subGaussianBudgetRadius_nonneg theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:833
BanditRLProof.UCB.subGaussianBudgetRadius_sq_domination theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:847
BanditRLProof.UCB.subGaussianOneSidedDeviationTail_budgetRadius_le_exp_neg_budget theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:861
BanditRLProof.UCB.measure_upperConfidenceBad_le_subGaussian_tail theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:874
BanditRLProof.UCB.measure_upperConfidenceBad_le_subGaussian_exp_neg_budget theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:926
BanditRLProof.UCB.measure_upperConfidenceBad_le_subGaussian_budgetRadius theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:956
BanditRLProof.UCB.measure_lowerConfidenceBad_le_subGaussian_tail theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:979
BanditRLProof.UCB.measure_lowerConfidenceBad_le_subGaussian_exp_neg_budget theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1029
BanditRLProof.UCB.measure_lowerConfidenceBad_le_subGaussian_budgetRadius theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1059
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_subGaussian_oneSided_tail_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1090
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_subGaussian_exp_neg_budget_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1130
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_subGaussian_budgetRadius_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1176
BanditRLProof.UCB.exp_neg_log_eq_inv theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1212
BanditRLProof.UCB.subGaussianLogBudgetRadius definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1222
BanditRLProof.UCB.subGaussianLogBudgetRadius_apply theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1228
BanditRLProof.UCB.subGaussianLogBudgetRadius_nonneg theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1237
BanditRLProof.UCB.subGaussianLogBudgetRadius_sq_domination theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1250
BanditRLProof.UCB.subGaussianOneSidedDeviationTail_logBudgetRadius_le_inv_scale theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1264
BanditRLProof.UCB.measure_upperConfidenceBad_le_subGaussian_logBudgetRadius theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1282
BanditRLProof.UCB.measure_lowerConfidenceBad_le_subGaussian_logBudgetRadius theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1309
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_subGaussian_logBudgetRadius_inv_scale_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1340
BanditRLProof.UCB.subGaussianConstantLogBudgetRadius definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1387
BanditRLProof.UCB.subGaussianConstantLogBudgetRadius_apply theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1393
BanditRLProof.UCB.subGaussianConstantLogBudgetRadius_nonneg theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1402
BanditRLProof.UCB.subGaussianConstantLogBudgetRadius_sq_domination theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1414
BanditRLProof.UCB.constant_invScale_double_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1427
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_subGaussian_constantLogBudgetRadius_card theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1443
BanditRLProof.UCB.constant_invScale_double_sum_le_of_real theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1480
BanditRLProof.UCB.textbookDeltaScale definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1508
BanditRLProof.UCB.textbookDeltaScale_pos theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1513
BanditRLProof.UCB.textbookDeltaScale_total_inv_budget_eq_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1525
BanditRLProof.UCB.constant_invScale_double_sum_textbookDeltaScale_le_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1548
BanditRLProof.UCB.subGaussianTextbookDeltaRadius definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1564
BanditRLProof.UCB.subGaussianTextbookDeltaRadius_apply theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1571
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_subGaussian_textbookDeltaRadius_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1584
BanditRLProof.UCB.measure_scoreMaxEvent_le_subGaussian_textbookDeltaRadius_delta_of_gap theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1617
BanditRLProof.UCB.selectedEvent_subset_scoreMaxEvent_of_action_score_max theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1662
BanditRLProof.UCB.measure_selectedLargeGapEvent_le_subGaussian_textbookDeltaRadius_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1688
BanditRLProof.UCB.selectedEventOn_subset_finiteHorizonConfidenceBadEvent_of_action_score_max theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1737
BanditRLProof.UCB.measure_selectedLargeGapEventOn_le_subGaussian_textbookDeltaRadius_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1769
BanditRLProof.UCB.measure_confidenceScoreArgmax_selectedLargeGapEvent_le_subGaussian_textbookDeltaRadius_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1815
BanditRLProof.UCB.measure_confidenceScoreArgmax_selectedLargeGapEventOn_le_subGaussian_textbookDeltaRadius_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1857
BanditRLProof.UCB.sum_measure_confidenceScoreArgmax_selectedLargeGapEventOn_le_card_mul_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1905
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_selectedLargeGapCountOn_le_card_mul_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:1960
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_horizon_mul_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2016
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_free_or_delta_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2074
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_freeBudget_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2145
BanditRLProof.UCB.freeTimes_indicator_sum_le_card theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2226
BanditRLProof.UCB.selectedSmallPullCount_sum_eq_min_pullCount theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2256
BanditRLProof.UCB.selectedSmallPullCount_sum_le_threshold theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2316
BanditRLProof.UCB.selectedSmallPullCount_indicator_sum_le_threshold theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2331
BanditRLProof.UCB.lintegral_selectedSmallPullCount_indicator_sum_le_threshold theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2361
BanditRLProof.UCB.selectedPullCount_sum_eq_pullCount theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2398
BanditRLProof.UCB.selectedPullCount_indicator_sum_eq_natCast_pullCount theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2422
BanditRLProof.UCB.selectedPullCount_indicator_sum_eq_selectedSmall_add_selectedLargePullCount theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2441
BanditRLProof.UCB.natCast_pullCount_le_threshold_add_selectedLargePullCount_indicator_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2483
BanditRLProof.UCB.measurableSet_selectedLargePullCount theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2533
BanditRLProof.UCB.lintegral_selectedLargePullCount_indicator_sum_eq_sum_measure theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2555
BanditRLProof.UCB.measure_confidenceScoreArgmax_selectedLargePullCountEvent_le_subGaussian_textbookDeltaRadius_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2667
BanditRLProof.UCB.sum_measure_confidenceScoreArgmax_selectedLargePullCountEvent_le_horizon_mul_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2739
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_selectedLargePullCount_indicator_sum_le_horizon_mul_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2807
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_threshold_add_horizon_delta_of_selectedLargePullCount theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2870
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_freeCard_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:2960
BanditRLProof.UCB.subGaussianTextbookDeltaRadiusChargedTimes definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3003
BanditRLProof.UCB.subGaussianTextbookDeltaRadiusFreeTimes definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3018
BanditRLProof.UCB.mem_subGaussianTextbookDeltaRadiusChargedTimes_iff theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3027
BanditRLProof.UCB.mem_subGaussianTextbookDeltaRadiusFreeTimes_iff theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3038
BanditRLProof.UCB.subGaussianTextbookDeltaRadiusChargedTimes_of_not_free theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3049
BanditRLProof.UCB.subGaussianTextbookDeltaRadiusChargedTimes_gap_large theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3066
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_textbookDeltaRadiusFreeCard_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3086
BanditRLProof.UCB.subGaussianTextbookDeltaRadiusFreeTimes_card_le_threshold theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3141
BanditRLProof.UCB.subGaussianTextbookDeltaRadiusFreeTimes_card_le_threshold_ennreal theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3168
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_textbookDeltaRadiusThreshold_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3189
BanditRLProof.UCB.subGaussianTextbookDeltaRadius_large_gap_of_lt_half_meanGap theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3236
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_textbookDeltaRadiusHalfGapThreshold_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3255
BanditRLProof.UCB.subGaussianTextbookDeltaRadius_lt_half_meanGap_of_sq_lt theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3301
BanditRLProof.UCB.subGaussianTextbookDeltaRadius_lt_half_meanGap_of_eight_mul_lt_sq theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3321
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_textbookDeltaRadiusEightProxyLogThreshold_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3350
BanditRLProof.UCB.subGaussianTextbookDeltaRadius_lt_half_meanGap_of_proxy_lt_gap_sq_div theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3400
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_textbookDeltaRadiusProxyThreshold_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3446
BanditRLProof.UCB.subGaussianTextbookDeltaRadius_lt_half_meanGap_of_proxy_le_variance_div_count theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3498
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_textbookDeltaRadiusSampleCountThreshold_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3542
BanditRLProof.UCB.subGaussianTextbookDeltaRadius_count_large_of_threshold_lt_bound theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3602
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_textbookDeltaRadiusSampleCountLowerBound_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3637
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_textbookDeltaRadiusRecursiveSampleCount_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3704
BanditRLProof.UCB.lintegral_confidenceScoreArgmax_pullCount_le_textbookDeltaRadiusSampleCountSource_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3801
BanditRLProof.UCB.lintegral_historyAction_pullCount_le_textbookDeltaRadiusSampleCountSource_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:3888
BanditRLProof.UCB.lintegral_generatedActionTrace_pullCount_le_textbookDeltaRadiusSampleCountSource_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:4009
BanditRLProof.UCB.identityActionPolicy definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:4086
BanditRLProof.UCB.confidenceScoreArgmaxGeneratedState definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:4099
BanditRLProof.UCB.confidenceScoreArgmaxGeneratedTrace definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:4109
BanditRLProof.UCB.lintegral_confidenceScoreArgmaxGeneratedTrace_pullCount_le_textbookDeltaRadiusSampleCountSource_add_horizon_delta theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:4126
BanditRLProof.UCB.subGaussianAbsDeviationTail definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:4202
BanditRLProof.UCB.measure_absDeviation_le_subGaussian_tail theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:4214
BanditRLProof.UCB.measure_finiteHorizonConfidenceBadEvent_le_subGaussian_tail_sum theorem UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:4298
BanditRLProof.UCB.obligationNames definition UCB BanditRLProof.Algorithms.UCB Compiled BanditRLProof/Algorithms/UCB.lean:4327
BanditRLProof.UCB.armStreamPSeriesTerm definition UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:23
BanditRLProof.UCB.armStreamPSeriesTailBound definition UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:27
BanditRLProof.UCB.armStreamPSeriesTerm_summable theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:30
BanditRLProof.UCB.indexTail_four_eq_coe_armStreamPSeriesTerm theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:35
BanditRLProof.UCB.constSum_four_le_armStreamPSeriesTailBound theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:40
BanditRLProof.UCB.constSum_four_toReal_le_armStreamPSeriesTailBound theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:52
BanditRLProof.UCB.armStreamAsymptoticModelCoefficient definition UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:62
BanditRLProof.UCB.armStreamAsymptoticModelCoefficient_nonneg theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:69
BanditRLProof.UCB.lml_sum_four_le_armStreamAsymptoticModelCoefficient theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:86
BanditRLProof.UCB.armStreamExpectedRegret definition UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:149
BanditRLProof.UCB.armStreamExpectedRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:157
BanditRLProof.UCB.armStreamExpectedRegret_isBigO_log theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:182
BanditRLProof.UCB.armStreamExpectedRegret_isLittleO_natCast_succ theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:223
BanditRLProof.UCB.armStreamExpectedAverageRegret definition UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:236
BanditRLProof.UCB.armStreamExpectedAverageRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBArmStreamAsymptotics Compiled BanditRLProof/Algorithms/UCBArmStreamAsymptotics.lean:245
BanditRLProof.UCB.armStreamCoordinate definition UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:21
BanditRLProof.UCB.armStreamWithoutCoordinate definition UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:26
BanditRLProof.UCB.armStreamInsertCoordinate definition UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:31
BanditRLProof.UCB.armStreamHistoryAction definition UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:38
BanditRLProof.UCB.armStreamNextCoordinate definition UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:47
BanditRLProof.UCB.armStreamCoordinateOfHistoryAction definition UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:55
BanditRLProof.UCB.armStreamHistoryActionCoordinateBranch definition UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:62
BanditRLProof.UCB.armStreamSelectedRewardKernel abbreviation UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:68
BanditRLProof.UCB.armStreamNextCoordinateBranch definition UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:74
BanditRLProof.UCB.armStreamHistoryActionFromWithout definition UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:80
BanditRLProof.UCB.measurable_armStreamCoordinate theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:87
BanditRLProof.UCB.measurable_armStreamWithoutCoordinate theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:92
BanditRLProof.UCB.measurable_armStreamInsertCoordinate theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:98
BanditRLProof.UCB.armStreamWithoutCoordinate_insertCoordinate theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:113
BanditRLProof.UCB.measurable_armStreamHistoryAction theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:122
BanditRLProof.UCB.measurable_armStreamNextCoordinate theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:129
BanditRLProof.UCB.measurable_armStreamCoordinateOfHistoryAction theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:142
BanditRLProof.UCB.measurableSet_armStreamHistoryActionCoordinateBranch theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:154
BanditRLProof.UCB.measurableSet_armStreamNextCoordinateBranch theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:160
BanditRLProof.UCB.armStreamNextCoordinate_eq_coordinateOfHistoryAction theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:167
BanditRLProof.UCB.pairwise_disjoint_armStreamHistoryActionCoordinateBranch theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:175
BanditRLProof.UCB.pairwise_disjoint_armStreamNextCoordinateBranch theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:191
BanditRLProof.UCB.iUnion_armStreamHistoryActionCoordinateBranch theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:206
BanditRLProof.UCB.iUnion_armStreamNextCoordinateBranch theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:213
BanditRLProof.UCB.measure_eq_sum_restrict_armStreamHistoryActionCoordinateBranch theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:220
BanditRLProof.UCB.armStreamMeasure_eq_sum_restrict_nextCoordinateBranch theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:232
BanditRLProof.UCB.measurable_armStreamHistoryActionFromWithout theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:244
BanditRLProof.UCB.armStreamNextCoordinate_fst_eq_pullCount theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:252
BanditRLProof.UCB.armStreamReward_succ_eq_nextCoordinate theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:263
BanditRLProof.UCB.armStreamHistory_eq_of_eq_below_pullCount theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:279
BanditRLProof.UCB.armStreamHistory_eq_of_withoutCoordinate_eq_of_pullCount_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:328
BanditRLProof.UCB.armStreamNextCoordinate_eq_iff_insertCoordinate theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:350
BanditRLProof.UCB.armStreamHistoryAction_eq_fromWithout_of_nextCoordinate_eq theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:384
BanditRLProof.UCB.iIndepFun_armStreamMeasure_coordinate theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:405
BanditRLProof.UCB.indepFun_armStreamMeasure_coordinate_without theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:417
BanditRLProof.UCB.indepFun_armStreamMeasure_coordinate_historyActionFromWithout theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:459
BanditRLProof.UCB.armStreamMeasure_map_historyActionFromWithout_coordinate_eq_prod theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:478
BanditRLProof.UCB.armStreamHistoryActionFromWithout_mem_coordinateBranch_iff theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:511
BanditRLProof.UCB.map_historyActionFromWithout_restrict_coordinateBranch_eq_historyAction theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:528
BanditRLProof.UCB.armStreamMeasure_map_historyAction_reward_restrict_branch_eq_prod theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:577
BanditRLProof.UCB.armStreamMeasure_map_historyAction_reward_succ_eq_compProd theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:657
BanditRLProof.UCB.armStreamReward_succ_condDistrib_ae_eq_nu theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:756
BanditRLProof.UCB.canonicalArmStreamHistoryEnvironment_feedback_ae_eq_nu theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:777
BanditRLProof.UCB.armStreamMeasure_condDistrib_coordinate_given_without theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:805
BanditRLProof.UCB.armStreamReward_zero_condDistrib_ae_eq_nu theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:830
BanditRLProof.UCB.canonicalArmStreamHistoryEnvironment_initialFeedback_ae_eq_nu theorem UCB BanditRLProof.Algorithms.UCBArmStreamConditionalReward Compiled BanditRLProof/Algorithms/UCBArmStreamConditionalReward.lean:882
BanditRLProof.UCB.armStreamAction_eq_initializationArm_of_lt theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:26
BanditRLProof.UCB.pullCount_armStreamAction_K_eq_one theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:38
BanditRLProof.UCB.pullCount_armStreamAction_pos_of_K_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:61
BanditRLProof.UCB.K_lt_of_one_lt_pullCount_armStreamAction theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:71
BanditRLProof.UCB.armStreamAction_eq_realIndexAction_of_K_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:84
BanditRLProof.UCB.realIndex_le_realIndex_armStreamAction_of_K_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:107
BanditRLProof.UCB.meanGap_le_two_realWidth_of_selected theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:120
BanditRLProof.UCB.pullCount_le_eight_scale_log_div_gap_sq theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:146
BanditRLProof.UCB.realPullThreshold definition UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:173
BanditRLProof.UCB.pullThreshold definition UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:178
BanditRLProof.UCB.indexTail definition UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:183
BanditRLProof.UCB.constSum definition UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:187
BanditRLProof.UCB.selectedLargePullCountEvent definition UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:191
BanditRLProof.UCB.lowerIndexFailure definition UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:200
BanditRLProof.UCB.upperIndexFailure definition UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:214
BanditRLProof.UCB.selectedLargePullCountEvent_subset_lower_union_upper theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:232
BanditRLProof.UCB.measure_selectedLargePullCountEvent_le_two_mul_indexTail theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:375
BanditRLProof.UCB.lintegral_selectedLargePullCount_indicator_sum_le_two_mul_constSum theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:423
BanditRLProof.UCB.lintegral_natCast_pullCount_armStreamAction_le_threshold_add_two_mul_constSum theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:473
BanditRLProof.UCB.indexTail_ne_top theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:538
BanditRLProof.UCB.constSum_ne_top theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:543
BanditRLProof.UCB.integrable_real_pullCount_armStreamAction theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:548
BanditRLProof.UCB.integral_real_pullCount_armStreamAction_le_threshold_add_two_mul_constSum theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:567
BanditRLProof.UCB.pullThreshold_cast_le_realPullThreshold_add_two theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:635
BanditRLProof.UCB.integral_real_pullCount_armStreamAction_le_realThreshold_add_two_add_two_mul_constSum theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:646
BanditRLProof.UCB.integral_realKernelRegret_armStreamAction_le_sum_gap_mul_realThreshold_add_two_add_two_mul_constSum theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:675
BanditRLProof.UCB.integral_realKernelRegret_armStreamAction_le_lml_sum theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:718
BanditRLProof.UCB.measurable_armStreamActionTrace theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:743
BanditRLProof.UCB.measurable_realKernelRegret_actionTrace theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:750
BanditRLProof.UCB.integral_realKernelRegret_externalAction_le_lml_sum_of_identDistrib_armStreamAction theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:769
BanditRLProof.UCB.identDistrib_action_armStreamAction_of_identDistrib_armStream theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:801
BanditRLProof.UCB.integral_realKernelRegret_externalAction_le_lml_sum_of_identDistrib_armStream theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:829
BanditRLProof.UCB.identDistrib_action_of_identDistrib_actionRewardTrace theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:862
BanditRLProof.UCB.integral_realKernelRegret_externalAction_le_lml_sum_of_identDistrib_actionRewardTrace theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:885
BanditRLProof.UCB.integral_realKernelRegret_externalAction_le_lml_sum_of_common_actionReward_condDistrib theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:922
BanditRLProof.UCB.identDistrib_actionRewardTrace_of_condDistrib_eq_armStream theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:1011
BanditRLProof.UCB.identDistrib_actionRewardTrace_of_split_condDistrib_eq_armStream theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:1097
BanditRLProof.UCB.integral_realKernelRegret_externalAction_le_lml_sum_of_split_condDistrib_eq_armStream theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:1251
BanditRLProof.UCB.integral_realKernelRegret_externalAction_le_lml_sum_of_condDistrib_eq_armStream theorem UCB BanditRLProof.Algorithms.UCBArmStreamExpectedPullCount Compiled BanditRLProof/Algorithms/UCBArmStreamExpectedPullCount.lean:1332
BanditRLProof.UCB.finiteArmRealRewardKernel definition UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:21
BanditRLProof.UCB.finiteArmRealRewardKernel_apply theorem UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:26
BanditRLProof.UCB.finiteArmRealRewardKernel_isMarkov theorem UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:32
BanditRLProof.UCB.armStreamFiniteArmSubgaussianExpectedRegret definition UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:44
BanditRLProof.UCB.armStreamFiniteArmSubgaussianExpectedRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:55
BanditRLProof.UCB.armStreamFiniteArmSubgaussianExpectedAverageRegret definition UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:95
BanditRLProof.UCB.armStreamFiniteArmSubgaussianExpectedAverageRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:108
BanditRLProof.UCB.armStreamBoundedFiniteArmExpectedRegret definition UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:145
BanditRLProof.UCB.armStreamBoundedFiniteArmExpectedRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:154
BanditRLProof.UCB.armStreamBoundedFiniteArmExpectedAverageRegret definition UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:188
BanditRLProof.UCB.armStreamBoundedFiniteArmExpectedAverageRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:201
BanditRLProof.UCB.armStreamArmwiseBoundedFiniteArmExpectedRegret definition UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:231
BanditRLProof.UCB.armStreamArmwiseBoundedFiniteArmExpectedRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:240
BanditRLProof.UCB.armStreamArmwiseBoundedFiniteArmExpectedAverageRegret definition UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:279
BanditRLProof.UCB.armStreamArmwiseBoundedFiniteArmExpectedAverageRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBArmStreamFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBArmStreamFiniteArmRewardLaws.lean:293
BanditRLProof.UCB.initializationArm definition UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:20
BanditRLProof.UCB.initializationArm_zero theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:24
BanditRLProof.UCB.realHistoryNextArm definition UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:34
BanditRLProof.UCB.measurable_realHistoryNextArm theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:43
BanditRLProof.UCB.measurable_armRewardStream_apply theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:53
BanditRLProof.UCB.armStreamHistory definition UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:66
BanditRLProof.UCB.armStreamAction definition UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:80
BanditRLProof.UCB.armStreamReward definition UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:88
BanditRLProof.UCB.armStreamAction_zero theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:94
BanditRLProof.UCB.armStreamAction_succ theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:100
BanditRLProof.UCB.armStreamHistory_eq_finitePairHistoryOfTrace theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:111
BanditRLProof.UCB.measurable_armStreamHistory theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:141
BanditRLProof.UCB.measurable_armStreamAction theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:217
BanditRLProof.UCB.measurable_armStreamReward theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:227
BanditRLProof.UCB.armStreamAction_succ_eq_realHistoryNextArm_actualHistory theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:246
BanditRLProof.UCB.armStreamAction_succ_eq_realHistoryIndexAction_of_not_lt theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:257
BanditRLProof.UCB.armStreamUCBFixedArmPrefixSource definition UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:269
BanditRLProof.UCB.armStreamMeasure definition UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:276
BanditRLProof.UCB.measure_pullCount_prod_sumRewards_armStreamUCB_mem_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamProcess Compiled BanditRLProof/Algorithms/UCBArmStreamProcess.lean:291
BanditRLProof.UCB.rewardFromArmStream definition UCB BanditRLProof.Algorithms.UCBArmStreamSource Compiled BanditRLProof/Algorithms/UCBArmStreamSource.lean:28
BanditRLProof.UCB.sumRewards_rewardFromArmStream_eq_armPrefixSum theorem UCB BanditRLProof.Algorithms.UCBArmStreamSource Compiled BanditRLProof/Algorithms/UCBArmStreamSource.lean:42
BanditRLProof.UCB.fixedArmPrefixSourceOfArmStream definition UCB BanditRLProof.Algorithms.UCBArmStreamSource Compiled BanditRLProof/Algorithms/UCBArmStreamSource.lean:65
BanditRLProof.UCB.measure_pullCount_prod_sumRewards_rewardFromArmStream_mem_le_identDistrib theorem UCB BanditRLProof.Algorithms.UCBArmStreamSource Compiled BanditRLProof/Algorithms/UCBArmStreamSource.lean:81
BanditRLProof.UCB.canonicalFixedArmPrefixSource definition UCB BanditRLProof.Algorithms.UCBArmStreamSource Compiled BanditRLProof/Algorithms/UCBArmStreamSource.lean:109
BanditRLProof.UCB.measure_pullCount_prod_sumRewards_rewardFromCanonicalArmStream_mem_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamSource Compiled BanditRLProof/Algorithms/UCBArmStreamSource.lean:121
BanditRLProof.UCB.armStreamMeasure_map_coord theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:21
BanditRLProof.UCB.iIndepFun_armStreamMeasure_coord_sub theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:45
BanditRLProof.UCB.iIndepFun_armStreamMeasure_sub_coord theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:59
BanditRLProof.UCB.hasSubgaussianMGF_armStreamMeasure_coord_sub theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:73
BanditRLProof.UCB.hasSubgaussianMGF_armStreamMeasure_sub_coord theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:92
BanditRLProof.UCB.sum_coord_sub_eq_armPrefixSum_sub theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:108
BanditRLProof.UCB.sum_sub_coord_eq_mul_sub_armPrefixSum theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:115
BanditRLProof.UCB.measure_armPrefixSum_sub_mul_ge_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:123
BanditRLProof.UCB.measure_mul_sub_armPrefixSum_ge_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:146
BanditRLProof.UCB.armPrefixEmpiricalMean definition UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:169
BanditRLProof.UCB.armPrefixAverageConfidenceRadius definition UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:177
BanditRLProof.UCB.measure_armPrefixAverageConfidenceRadius_le_abs_empiricalMean_sub theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:188
BanditRLProof.UCB.upperDeviationPairs definition UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:243
BanditRLProof.UCB.lowerDeviationPairs definition UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:248
BanditRLProof.UCB.positiveUpperDeviationPairs definition UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:253
BanditRLProof.UCB.positiveLowerDeviationPairs definition UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:259
BanditRLProof.UCB.mem_fst_image_upperDeviationPairs theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:265
BanditRLProof.UCB.mem_fst_image_lowerDeviationPairs theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:274
BanditRLProof.UCB.mem_fst_image_positiveUpperDeviationPairs_iff theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:283
BanditRLProof.UCB.mem_fst_image_positiveLowerDeviationPairs_iff theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:298
BanditRLProof.UCB.measure_sumRewards_sub_pullCount_mul_ge_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:319
BanditRLProof.UCB.measure_pullCount_mul_sub_sumRewards_ge_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:364
BanditRLProof.UCB.measure_pos_and_sumRewards_sub_pullCount_mul_ge_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:409
BanditRLProof.UCB.measure_pos_and_pullCount_mul_sub_sumRewards_ge_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:467
BanditRLProof.UCB.countWidthThreshold definition UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:525
BanditRLProof.UCB.countWidthThreshold_nonneg theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:532
BanditRLProof.UCB.countWidthThreshold_le_mul_mean_sub_sumRewards_of_empiricalMean_add_width_le theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:538
BanditRLProof.UCB.countWidthThreshold_le_sumRewards_sub_mul_mean_of_mean_le_empiricalMean_sub_width theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:566
BanditRLProof.UCB.measure_realEmpiricalMean_add_realWidth_le_mean theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:597
BanditRLProof.UCB.measure_mean_le_realEmpiricalMean_sub_realWidth theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:661
BanditRLProof.UCB.countWidthThreshold_sq_div_eq theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:723
BanditRLProof.UCB.positiveCountFilter_eq_Icc theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:745
BanditRLProof.UCB.sum_countWidthThreshold_tail_eq theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:752
BanditRLProof.UCB.natCast_mul_exp_neg_log_le_inv_rpow_sub_one theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:780
BanditRLProof.UCB.measure_realEmpiricalMean_add_realWidth_le_mean_log_bound theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:826
BanditRLProof.UCB.measure_mean_le_realEmpiricalMean_sub_realWidth_log_bound theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:851
BanditRLProof.UCB.measure_realEmpiricalMean_add_realWidth_le_mean_rpow_bound theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:877
BanditRLProof.UCB.measure_mean_le_realEmpiricalMean_sub_realWidth_rpow_bound theorem UCB BanditRLProof.Algorithms.UCBArmStreamTail Compiled BanditRLProof/Algorithms/UCBArmStreamTail.lean:900
BanditRLProof.UCB.selectedPolicySuccessorArmwiseBoundedFiniteArmExpectedPseudoRegret definition UCB BanditRLProof.Algorithms.UCBArmwiseBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBArmwiseBoundedFiniteArmSampledAsymptotics.lean:24
BanditRLProof.UCB.selectedPolicySuccessorArmwiseBoundedFiniteArmExpectedPseudoRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBArmwiseBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBArmwiseBoundedFiniteArmSampledAsymptotics.lean:42
BanditRLProof.UCB.selectedPolicySuccessorArmwiseBoundedFiniteArmExpectedPseudoRegret_isBigO_log theorem UCB BanditRLProof.Algorithms.UCBArmwiseBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBArmwiseBoundedFiniteArmSampledAsymptotics.lean:87
BanditRLProof.UCB.selectedPolicySuccessorArmwiseBoundedFiniteArmExpectedPseudoRegret_isLittleO_natCast_succ theorem UCB BanditRLProof.Algorithms.UCBArmwiseBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBArmwiseBoundedFiniteArmSampledAsymptotics.lean:126
BanditRLProof.UCB.selectedPolicySuccessorArmwiseBoundedFiniteArmExpectedAveragePseudoRegret definition UCB BanditRLProof.Algorithms.UCBArmwiseBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBArmwiseBoundedFiniteArmSampledAsymptotics.lean:153
BanditRLProof.UCB.selectedPolicySuccessorArmwiseBoundedFiniteArmExpectedAveragePseudoRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBArmwiseBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBArmwiseBoundedFiniteArmSampledAsymptotics.lean:175
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_boundedFiniteArmLaws theorem UCB BanditRLProof.Algorithms.UCBBoundedFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/UCBBoundedFiniteArmRewardLaw.lean:26
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_armwiseBoundedFiniteArmLaws theorem UCB BanditRLProof.Algorithms.UCBBoundedFiniteArmRewardLaw Compiled BanditRLProof/Algorithms/UCBBoundedFiniteArmRewardLaw.lean:115
BanditRLProof.UCB.selectedPolicySuccessorBoundedFiniteArmExpectedPseudoRegret definition UCB BanditRLProof.Algorithms.UCBBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBBoundedFiniteArmSampledAsymptotics.lean:24
BanditRLProof.UCB.selectedPolicySuccessorBoundedFiniteArmExpectedPseudoRegret_isBigO_log theorem UCB BanditRLProof.Algorithms.UCBBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBBoundedFiniteArmSampledAsymptotics.lean:38
BanditRLProof.UCB.selectedPolicySuccessorBoundedFiniteArmExpectedPseudoRegret_isLittleO_natCast_succ theorem UCB BanditRLProof.Algorithms.UCBBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBBoundedFiniteArmSampledAsymptotics.lean:79
BanditRLProof.UCB.selectedPolicySuccessorBoundedFiniteArmExpectedAveragePseudoRegret definition UCB BanditRLProof.Algorithms.UCBBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBBoundedFiniteArmSampledAsymptotics.lean:105
BanditRLProof.UCB.selectedPolicySuccessorBoundedFiniteArmExpectedAveragePseudoRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBBoundedFiniteArmSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBBoundedFiniteArmSampledAsymptotics.lean:126
BanditRLProof.UCB.selectedPolicySuccessorEmpiricalMeanAt definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLaw Compiled BanditRLProof/Algorithms/UCBConditionalRewardLaw.lean:22
BanditRLProof.UCB.selectedPolicySuccessorRadiusAt definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLaw Compiled BanditRLProof/Algorithms/UCBConditionalRewardLaw.lean:31
BanditRLProof.UCB.selectedPolicySuccessorIndexAt definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLaw Compiled BanditRLProof/Algorithms/UCBConditionalRewardLaw.lean:43
BanditRLProof.UCB.SelectedPolicySuccessorInitializedScoreMaxSource structure UCB BanditRLProof.Algorithms.UCBConditionalRewardLaw Compiled BanditRLProof/Algorithms/UCBConditionalRewardLaw.lean:63
BanditRLProof.UCB.selectedPolicySuccessorLargeGapEvent definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLaw Compiled BanditRLProof/Algorithms/UCBConditionalRewardLaw.lean:88
BanditRLProof.UCB.SelectedPolicySuccessorInitializedScoreMaxSource.meanGap_le_two_radius_of_not_badEvent theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLaw Compiled BanditRLProof/Algorithms/UCBConditionalRewardLaw.lean:106
BanditRLProof.UCB.measure_selectedPolicySuccessorLargeGapEvent_le_ennreal_delta_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLaw Compiled BanditRLProof/Algorithms/UCBConditionalRewardLaw.lean:189
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_selected_policy_centeredKernel_of_variance_le theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:17
BanditRLProof.ConditionalExpectationReward.armMaskedCenteredRewardSuccProcess_sum_abs_tail_predictableVariance_ennreal_delta_of_reward_map_eq_selected_policy_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:183
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMean_abs_tail_exact_pullCount_ennreal_delta_of_reward_map_eq_selected_policy_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:367
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMean_abs_tail_random_pullCount_ennreal_delta_of_reward_map_eq_selected_policy_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:572
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMean_simultaneous_finiteArmTime_abs_tail_ennreal_delta_of_reward_map_eq_selected_policy_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:698
BanditRLProof.UCB.measure_selectedPolicySuccessorLargeGapEvent_le_ennreal_delta_of_reward_map_eq_selected_policy_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:841
BanditRLProof.UCB.SelectedPolicySuccessorRewardMapLaw definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:950
BanditRLProof.UCB.measure_selectedPolicySuccessorLargeGapEvent_generatedUCB_le_ennreal_delta_of_reward_map_eq_selected_policy_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:1009
BanditRLProof.UCB.lintegral_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_le_explicitPullThreshold_add_horizon_mul_delta_of_reward_map_eq_selected_policy_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:1095
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_explicitThresholdSum_of_reward_map_eq_selected_policy_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:1174
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_of_reward_map_eq_selected_policy_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:1280
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_trajMeasure_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernel Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernel.lean:1361
BanditRLProof.UCB.selectedPolicySuccessorTextbookGapBudget_nonneg theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernelReal Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernelReal.lean:12
BanditRLProof.UCB.integrable_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernelReal Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernelReal.lean:28
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_trajMeasure_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawCenteredKernelReal Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawCenteredKernelReal.lean:62
BanditRLProof.UCB.SelectedPolicySuccessorFiniteHistoryState structure UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:20
BanditRLProof.UCB.completeFinitePairHistory definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:29
BanditRLProof.UCB.completeFinitePairHistoryAction definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:41
BanditRLProof.UCB.completeFinitePairHistoryReward definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:49
BanditRLProof.UCB.completeFinitePairHistory_finitePairHistoryOfTrace_apply_of_le theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:57
BanditRLProof.UCB.selectedPolicySuccessorHistoryIndex definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:69
BanditRLProof.UCB.selectedPolicySuccessorHistoryNextArm definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:92
BanditRLProof.UCB.selectedPolicySuccessorHistoryIndex_le_nextArm_of_K_le theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:105
BanditRLProof.UCB.selectedPolicySuccessorPairHistory definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:127
BanditRLProof.UCB.selectedPolicySuccessorHistoryState definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:151
BanditRLProof.UCB.measurable_selectedPolicySuccessorHistoryState theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:162
BanditRLProof.UCB.selectedPolicySuccessorHistoryPolicy definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:172
BanditRLProof.UCB.selectedPolicySuccessorGeneratedUCBAction definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:185
BanditRLProof.UCB.selectedPolicySuccessorGeneratedUCBAction_succ theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:199
BanditRLProof.UCB.selectedPolicySuccessorPairHistory_eq_finitePairHistoryOfTrace theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:218
BanditRLProof.UCB.sumRewards_eq_of_forall_lt theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:269
BanditRLProof.UCB.successorArmPullCount_completeFinitePairHistory theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:292
BanditRLProof.UCB.successorArmRewardSum_completeFinitePairHistory theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:310
BanditRLProof.UCB.selectedPolicySuccessorHistoryIndex_finitePairHistoryOfTrace theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:334
BanditRLProof.UCB.selectedPolicySuccessorGeneratedUCBAction_succ_eq_initializationArm_of_lt theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:355
BanditRLProof.UCB.successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_K_add_one_eq_one theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:367
BanditRLProof.UCB.successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_pos_of_K_le theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:395
BanditRLProof.UCB.selectedPolicySuccessorGeneratedUCBInitializedScoreMaxSource definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:425
BanditRLProof.UCB.exists_selected_with_threshold_le_prior_pullCount theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:504
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmTimeLogBudget definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:524
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmTimeLogBudget_le_horizon theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:532
BanditRLProof.UCB.selectedPolicySuccessorRealPullThreshold definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:576
BanditRLProof.UCB.selectedPolicySuccessorPullThreshold definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:584
BanditRLProof.UCB.selectedPolicySuccessorPullThreshold_contracts theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:593
BanditRLProof.UCB.successorArmEmpiricalMeanFiniteArmTimePeelingRadius_eq theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:645
BanditRLProof.UCB.two_mul_successorArmEmpiricalMeanFiniteArmTimePeelingRadius_lt_gap theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:666
BanditRLProof.UCB.successorArmEmpiricalMeanFiniteArmTimePeelingRadius_lt_gap_of_threshold theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:721
BanditRLProof.UCB.successorArmEmpiricalMeanFiniteArmTimePeelingRadius_lt_gap_of_global_threshold theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:759
BanditRLProof.UCB.successorArmEmpiricalMeanFiniteArmTimePeelingRadius_lt_gap_of_explicitPullThreshold theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:794
BanditRLProof.UCB.K_le_of_selectedPolicySuccessorGeneratedUCBAction_selected_and_count_pos theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:818
BanditRLProof.UCB.measure_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_gt_threshold_le_of_largeGap theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:862
BanditRLProof.UCB.measure_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_gt_threshold_le_of_global_threshold theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:931
BanditRLProof.UCB.measure_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_gt_explicitPullThreshold_le_of_largeGap theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:974
BanditRLProof.UCB.measure_selectedPolicySuccessorLargeGapEvent_generatedUCB_le_ennreal_delta_of_reward_map_eq_selected_policy theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:1012
BanditRLProof.UCB.measure_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_gt_threshold_le_ennreal_delta_of_reward_map_eq_selected_policy theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:1152
BanditRLProof.UCB.measurable_selectedPolicySuccessorGeneratedUCBAction theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:1303
BanditRLProof.UCB.lintegral_natCast_le_threshold_add_bound_mul_of_measure_gt theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:1332
BanditRLProof.UCB.lintegral_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_le_threshold_add_horizon_mul_delta_of_largeGap theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:1386
BanditRLProof.UCB.lintegral_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_le_threshold_add_horizon_mul_delta_of_global_threshold theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:1446
BanditRLProof.UCB.lintegral_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_le_explicitPullThreshold_add_horizon_mul_delta_of_largeGap theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:1491
BanditRLProof.UCB.lintegral_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_le_explicitPullThreshold_add_horizon_mul_delta_of_reward_map_eq_selected_policy theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawPolicy Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawPolicy.lean:1531
BanditRLProof.UCB.modelMeanGap_bestArm_eq_realGap theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:19
BanditRLProof.UCB.selectedPolicySuccessorTextbookGapBudget definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:29
BanditRLProof.UCB.selectedPolicySuccessorPullThreshold_cast_le_realThreshold_add_two theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:37
BanditRLProof.UCB.gap_mul_selectedPolicySuccessorPullThreshold_cast_le_textbookGapBudget theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:55
BanditRLProof.UCB.ofReal_gap_mul_selectedPolicySuccessorPullThreshold_le_textbookGapBudget theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:93
BanditRLProof.UCB.sum_gap_mul_explicitThreshold_add_failure_le_textbookGapSum theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:111
BanditRLProof.UCB.selectedPolicySuccessorGeneratedUCBRegretAction definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:144
BanditRLProof.UCB.measurable_selectedPolicySuccessorGeneratedUCBRegretAction theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:154
BanditRLProof.UCB.pullCount_selectedPolicySuccessorGeneratedUCBRegretAction_eq theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:170
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_le_sum_gap_mul_bound_of_positiveGap_pullCount theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:191
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_explicitThresholdSum_of_reward_map_eq_selected_policy theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:262
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_of_reward_map_eq_selected_policy theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawRegret Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawRegret.lean:427
BanditRLProof.UCB.selectedPolicySuccessorRewardStepKernelFamily definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawTrajMeasure Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawTrajMeasure.lean:18
BanditRLProof.UCB.isMarkovKernel_selectedPolicySuccessorRewardStepKernelFamily theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawTrajMeasure Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawTrajMeasure.lean:37
BanditRLProof.UCB.selectedPolicySuccessorRewardTrajMeasure definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawTrajMeasure Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawTrajMeasure.lean:53
BanditRLProof.UCB.selectedPolicySuccessorGeneratedUCBSelectedRewardLawSource_trajMeasure definition UCB BanditRLProof.Algorithms.UCBConditionalRewardLawTrajMeasure Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawTrajMeasure.lean:99
BanditRLProof.UCB.selectedPolicySuccessorGeneratedUCB_reward_map_eq_selected_policy_trajMeasure theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawTrajMeasure Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawTrajMeasure.lean:157
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_trajMeasure theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardLawTrajMeasure Compiled BanditRLProof/Algorithms/UCBConditionalRewardLawTrajMeasure.lean:215
BanditRLProof.UCB.measure_actionRewardHistoryStepKernelFamily_selectedPolicySuccessorLargeGapEvent_le_ennreal_delta_trajMeasure theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectory Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectory.lean:34
BanditRLProof.UCB.measure_selectedPolicySuccessorLargeGapEvent_generatedUCB_le_ennreal_delta_actionRewardTrajMeasure_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectory Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectory.lean:163
BanditRLProof.UCB.measure_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_gt_explicitPullThreshold_le_ennreal_delta_actionRewardTrajMeasure_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectory Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectory.lean:361
BanditRLProof.UCB.lintegral_successorArmPullCount_selectedPolicySuccessorGeneratedUCBAction_le_explicitPullThreshold_add_horizon_mul_delta_actionRewardTrajMeasure_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectory Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectory.lean:485
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_explicitThresholdSum_actionRewardTrajMeasure_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectory Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectory.lean:613
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_actionRewardTrajMeasure_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectory Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectory.lean:778
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_actionRewardTrajMeasure_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectoryReal Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectoryReal.lean:18
BanditRLProof.UCB.selectedPolicySuccessorAsymptoticDelta definition UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:22
BanditRLProof.UCB.selectedPolicySuccessorAsymptoticDelta_pos theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:25
BanditRLProof.UCB.horizon_mul_selectedPolicySuccessorAsymptoticDelta_le_one theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:30
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmTimeLogBudget_asymptoticDelta_eq theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:39
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmTimeLogBudget_asymptoticDelta_le theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:55
BanditRLProof.UCB.selectedPolicySuccessorAsymptoticGapCoefficient definition UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:95
BanditRLProof.UCB.selectedPolicySuccessorTextbookGapBudget_add_failure_asymptoticDelta_le theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:99
BanditRLProof.UCB.selectedPolicySuccessorAsymptoticModelCoefficient definition UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:175
BanditRLProof.UCB.selectedPolicySuccessorTextbookGapSum_asymptoticDelta_le theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:182
BanditRLProof.UCB.selectedPolicySuccessorActionRewardTrajMeasureExpectedPseudoRegret definition UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:210
BanditRLProof.UCB.selectedPolicySuccessorActionRewardTrajMeasureExpectedPseudoRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:251
BanditRLProof.UCB.selectedPolicySuccessorAsymptoticModelCoefficient_nonneg theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:330
BanditRLProof.UCB.one_add_log_natCast_succ_isBigO_log_natCast_succ theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:342
BanditRLProof.UCB.selectedPolicySuccessorActionRewardTrajMeasureExpectedPseudoRegret_isBigO_log theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:363
BanditRLProof.UCB.log_natCast_succ_isLittleO_natCast_succ theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:425
BanditRLProof.UCB.selectedPolicySuccessorActionRewardTrajMeasureExpectedPseudoRegret_isLittleO_natCast_succ theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:434
BanditRLProof.UCB.selectedPolicySuccessorActionRewardTrajMeasureExpectedAveragePseudoRegret definition UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:465
BanditRLProof.UCB.selectedPolicySuccessorActionRewardTrajMeasureExpectedAveragePseudoRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledAsymptotics Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledAsymptotics.lean:482
BanditRLProof.UCB.actionRewardTrajectorySuccessorAction definition UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledReal Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledReal.lean:11
BanditRLProof.UCB.selectedPolicySuccessorGeneratedUCBRegretAction_ae_eq_actionRewardTrajectorySuccessorAction_trajMeasure theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledReal Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledReal.lean:21
BanditRLProof.UCB.integral_real_pseudoRegret_actionRewardTrajectorySuccessorAction_le_textbookGapSum_actionRewardTrajMeasure_centeredKernel theorem UCB BanditRLProof.Algorithms.UCBConditionalRewardPairTrajectorySampledReal Compiled BanditRLProof/Algorithms/UCBConditionalRewardPairTrajectorySampledReal.lean:136
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_trajMeasure_contextDependentBoundedRewardKernel theorem UCB BanditRLProof.Algorithms.UCBContextDependentBoundedRewardKernel Compiled BanditRLProof/Algorithms/UCBContextDependentBoundedRewardKernel.lean:25
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_trajMeasure_contextDependentSubgaussianRewardKernel theorem UCB BanditRLProof.Algorithms.UCBContextDependentSubGaussianRewardKernel Compiled BanditRLProof/Algorithms/UCBContextDependentSubGaussianRewardKernel.lean:30
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_trajMeasure_finiteContextDependentSubgaussianRewardKernel theorem UCB BanditRLProof.Algorithms.UCBContextDependentSubGaussianRewardKernel Compiled BanditRLProof/Algorithms/UCBContextDependentSubGaussianRewardKernel.lean:105
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_trajMeasure_finiteContextDependentSubgaussianRewardKernel_without_proxy_positivity theorem UCB BanditRLProof.Algorithms.UCBContextDependentSubGaussianRewardKernel Compiled BanditRLProof/Algorithms/UCBContextDependentSubGaussianRewardKernel.lean:176
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_finiteArmSubgaussianLaws theorem UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianRewardLaw Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianRewardLaw.lean:27
BanditRLProof.UCB.integral_real_pseudoRegret_selectedPolicySuccessorGeneratedUCBRegretAction_le_textbookGapSum_finiteArmSubgaussianLaws_without_proxy_positivity theorem UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianRewardLaw Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianRewardLaw.lean:119
BanditRLProof.UCB.finiteArmSubgaussianInitialActionRewardMeasure definition UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianSampledAsymptotics.lean:22
BanditRLProof.UCB.finiteArmSubgaussianInitialActionRewardMeasure_isProbabilityMeasure theorem UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianSampledAsymptotics.lean:28
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmSubgaussianExpectedPseudoRegret definition UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianSampledAsymptotics.lean:43
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmSubgaussianExpectedPseudoRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianSampledAsymptotics.lean:69
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmSubgaussianExpectedPseudoRegret_isBigO_log theorem UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianSampledAsymptotics.lean:142
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmSubgaussianExpectedPseudoRegret_isLittleO_natCast_succ theorem UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianSampledAsymptotics.lean:204
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmSubgaussianExpectedAveragePseudoRegret definition UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianSampledAsymptotics.lean:226
BanditRLProof.UCB.selectedPolicySuccessorFiniteArmSubgaussianExpectedAveragePseudoRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBFiniteArmSubGaussianSampledAsymptotics Compiled BanditRLProof/Algorithms/UCBFiniteArmSubGaussianSampledAsymptotics.lean:244
BanditRLProof.UCB.ArmRewardStream abbreviation UCB BanditRLProof.Algorithms.UCBFixedCountPeeling Compiled BanditRLProof/Algorithms/UCBFixedCountPeeling.lean:24
BanditRLProof.UCB.armPrefixSum definition UCB BanditRLProof.Algorithms.UCBFixedCountPeeling Compiled BanditRLProof/Algorithms/UCBFixedCountPeeling.lean:27
BanditRLProof.UCB.measurable_armPrefixSum theorem UCB BanditRLProof.Algorithms.UCBFixedCountPeeling Compiled BanditRLProof/Algorithms/UCBFixedCountPeeling.lean:32
BanditRLProof.UCB.FixedArmPrefixSource structure UCB BanditRLProof.Algorithms.UCBFixedCountPeeling Compiled BanditRLProof/Algorithms/UCBFixedCountPeeling.lean:45
BanditRLProof.UCB.FixedArmPrefixSource.measurable_armStream theorem UCB BanditRLProof.Algorithms.UCBFixedCountPeeling Compiled BanditRLProof/Algorithms/UCBFixedCountPeeling.lean:57
BanditRLProof.UCB.FixedArmPrefixSource.measurable_armPrefixSum theorem UCB BanditRLProof.Algorithms.UCBFixedCountPeeling Compiled BanditRLProof/Algorithms/UCBFixedCountPeeling.lean:68
BanditRLProof.UCB.measure_pullCount_prod_sumRewards_mem_le_of_fixedArmPrefixSource theorem UCB BanditRLProof.Algorithms.UCBFixedCountPeeling Compiled BanditRLProof/Algorithms/UCBFixedCountPeeling.lean:84
BanditRLProof.UCB.measure_pullCount_prod_sumRewards_mem_le_of_fixedArmPrefixSource_identDistrib theorem UCB BanditRLProof.Algorithms.UCBFixedCountPeeling Compiled BanditRLProof/Algorithms/UCBFixedCountPeeling.lean:147
BanditRLProof.UCB.selectedPolicySuccessorTelescopingRadiusAt definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:22
BanditRLProof.UCB.selectedPolicySuccessorTelescopingRadiusAt_nonneg theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:35
BanditRLProof.UCB.selectedPolicySuccessorTelescopingIndexAt definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:49
BanditRLProof.UCB.selectedPolicySuccessorTelescopingHistoryIndex definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:64
BanditRLProof.UCB.measurable_selectedPolicySuccessorTelescopingHistoryIndex theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:87
BanditRLProof.UCB.selectedPolicySuccessorTelescopingHistoryNextArm definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:96
BanditRLProof.UCB.selectedPolicySuccessorTelescopingHistoryIndex_le_nextArm_of_K_le theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:108
BanditRLProof.UCB.selectedPolicySuccessorTelescopingPairHistory definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:126
BanditRLProof.UCB.selectedPolicySuccessorTelescopingHistoryState definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:149
BanditRLProof.UCB.measurable_selectedPolicySuccessorTelescopingHistoryState theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:159
BanditRLProof.UCB.selectedPolicySuccessorTelescopingHistoryPolicy definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:168
BanditRLProof.UCB.selectedPolicySuccessorTelescopingGeneratedUCBAction definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:180
BanditRLProof.UCB.selectedPolicySuccessorTelescopingGeneratedUCBAction_succ theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:192
BanditRLProof.UCB.selectedPolicySuccessorTelescopingPairHistory_eq_finitePairHistoryOfTrace theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:210
BanditRLProof.UCB.selectedPolicySuccessorTelescopingHistoryIndex_finitePairHistoryOfTrace theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:261
BanditRLProof.UCB.selectedPolicySuccessorTelescopingIndexAt_le_generatedAction_of_K_le theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:283
BanditRLProof.UCB.selectedPolicySuccessorTelescopingGeneratedUCBAction_succ_eq_initializationArm_of_lt theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:330
BanditRLProof.UCB.successorArmPullCount_selectedPolicySuccessorTelescopingGeneratedUCBAction_K_add_one_eq_one theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:341
BanditRLProof.UCB.successorArmPullCount_selectedPolicySuccessorTelescopingGeneratedUCBAction_pos_of_K_le theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:369
BanditRLProof.UCB.K_le_of_selectedPolicySuccessorTelescopingGeneratedUCBAction_selected_and_count_pos theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:392
BanditRLProof.UCB.measurable_selectedPolicySuccessorTelescopingGeneratedUCBAction theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:426
BanditRLProof.UCB.selectedPolicySuccessorTelescopingLogBudget definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:448
BanditRLProof.UCB.selectedPolicySuccessorTelescopingLogBudget_eq theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:454
BanditRLProof.UCB.selectedPolicySuccessorTelescopingLogBudget_mono theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:468
BanditRLProof.UCB.successorArmEmpiricalMeanTelescopingPeelingRadius_eq theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:487
BanditRLProof.UCB.selectedPolicySuccessorTelescopingRealPullThreshold definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:507
BanditRLProof.UCB.selectedPolicySuccessorTelescopingPullThreshold definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:515
BanditRLProof.UCB.selectedPolicySuccessorTelescopingPullThreshold_contracts theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:523
BanditRLProof.UCB.two_mul_successorArmEmpiricalMeanTelescopingPeelingRadius_lt_gap_of_threshold theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:576
BanditRLProof.UCB.selectedPolicySuccessorTelescoping_meanGap_le_two_radius_of_not_badEvent theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:635
BanditRLProof.UCB.selectedPolicySuccessorTelescoping_pullCount_le_of_not_badEvent theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:712
BanditRLProof.UCB.actionRewardHistoryStepKernelFamily_selectedPolicySuccessorTelescoping_allTimeConfidence theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:790
BanditRLProof.UCB.measure_selectedPolicySuccessorTelescoping_pullCount_gt_threshold_le_of_allTimeConfidence theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:956
BanditRLProof.UCB.lintegral_selectedPolicySuccessorTelescoping_pullCount_le_of_allTimeConfidence theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:991
BanditRLProof.UCB.selectedPolicySuccessorTelescopingGeneratedUCBRegretAction definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:1050
BanditRLProof.UCB.measurable_selectedPolicySuccessorTelescopingGeneratedUCBRegretAction theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:1059
BanditRLProof.UCB.pullCount_selectedPolicySuccessorTelescopingGeneratedUCBRegretAction_eq theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:1072
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorTelescoping_le_of_allTimeConfidence theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:1091
BanditRLProof.UCB.selectedPolicySuccessorTelescoping_allHorizonPullCount_of_not_badEvent theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:1151
BanditRLProof.UCB.selectedPolicySuccessorTelescopingActionRewardTrajMeasure definition UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:1177
BanditRLProof.UCB.measure_selectedPolicySuccessorTelescoping_allTimeBadEvent_le_trajMeasure theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:1213
BanditRLProof.UCB.measure_selectedPolicySuccessorTelescoping_pullCount_gt_threshold_le_trajMeasure theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:1257
BanditRLProof.UCB.lintegral_ofReal_pseudoRegret_selectedPolicySuccessorTelescoping_le_trajMeasure theorem UCB BanditRLProof.Algorithms.UCBFixedPolicyTelescopingAnytimeRegret Compiled BanditRLProof/Algorithms/UCBFixedPolicyTelescopingAnytimeRegret.lean:1314
BanditRLProof.UCB.realEmpiricalMean definition UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:19
BanditRLProof.UCB.realWidth definition UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:25
BanditRLProof.UCB.realIndex definition UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:33
BanditRLProof.UCB.realHistoryWidth definition UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:39
BanditRLProof.UCB.realHistoryIndex definition UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:48
BanditRLProof.UCB.realIndexAction definition UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:56
BanditRLProof.UCB.realHistoryIndexAction definition UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:64
BanditRLProof.UCB.measurable_realHistoryPullCount theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:71
BanditRLProof.UCB.measurable_realHistorySumRewards theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:85
BanditRLProof.UCB.measurable_realHistoryEmpMean theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:99
BanditRLProof.UCB.measurable_realHistoryWidth theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:109
BanditRLProof.UCB.measurable_realHistoryIndex theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:119
BanditRLProof.UCB.measurable_realHistoryIndexAction theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:127
BanditRLProof.UCB.measurable_realEmpiricalMean theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:138
BanditRLProof.UCB.measurable_realWidth theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:153
BanditRLProof.UCB.measurable_realIndex theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:166
BanditRLProof.UCB.realIndexAction_spec theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:180
BanditRLProof.UCB.measurable_realIndexAction theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:191
BanditRLProof.UCB.realHistoryEmpiricalMean_finitePairHistoryOfTrace theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:207
BanditRLProof.UCB.realHistoryWidth_finitePairHistoryOfTrace theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:216
BanditRLProof.UCB.realHistoryIndex_finitePairHistoryOfTrace theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:226
BanditRLProof.UCB.realHistoryIndexAction_finitePairHistoryOfTrace theorem UCB BanditRLProof.Algorithms.UCBRealHistoryIndex Compiled BanditRLProof/Algorithms/UCBRealHistoryIndex.lean:237
BanditRLProof.UCB.RealStationaryUCBSequence structure UCB BanditRLProof.Algorithms.UCBRealLMLCompat Compiled BanditRLProof/Algorithms/UCBRealLMLCompat.lean:28
BanditRLProof.UCB.realStationaryUCBSequence_armStream theorem UCB BanditRLProof.Algorithms.UCBRealLMLCompat Compiled BanditRLProof/Algorithms/UCBRealLMLCompat.lean:88
BanditRLProof.UCB.identDistrib_actionRewardTrace_of_realStationaryUCBSequence theorem UCB BanditRLProof.Algorithms.UCBRealLMLCompat Compiled BanditRLProof/Algorithms/UCBRealLMLCompat.lean:109
BanditRLProof.UCB.regret_le_of_realStationaryUCBSequence theorem UCB BanditRLProof.Algorithms.UCBRealLMLCompat Compiled BanditRLProof/Algorithms/UCBRealLMLCompat.lean:136
BanditRLProof.UCB.canonicalArmStreamHistoryAlgorithm definition UCB BanditRLProof.Algorithms.UCBRealStationaryCanonicalKernelTrajectory Compiled BanditRLProof/Algorithms/UCBRealStationaryCanonicalKernelTrajectory.lean:22
BanditRLProof.UCB.canonicalArmStreamHistoryEnvironment definition UCB BanditRLProof.Algorithms.UCBRealStationaryCanonicalKernelTrajectory Compiled BanditRLProof/Algorithms/UCBRealStationaryCanonicalKernelTrajectory.lean:43
BanditRLProof.UCB.canonicalKernelTrajectoryMeasure definition UCB BanditRLProof.Algorithms.UCBRealStationaryCanonicalKernelTrajectory Compiled BanditRLProof/Algorithms/UCBRealStationaryCanonicalKernelTrajectory.lean:65
BanditRLProof.UCB.finiteArmCanonicalKernelTrajectoryMeasure definition UCB BanditRLProof.Algorithms.UCBRealStationaryCanonicalKernelTrajectory Compiled BanditRLProof/Algorithms/UCBRealStationaryCanonicalKernelTrajectory.lean:84
BanditRLProof.UCB.canonicalKernelTrajectoryAction definition UCB BanditRLProof.Algorithms.UCBRealStationaryCanonicalKernelTrajectory Compiled BanditRLProof/Algorithms/UCBRealStationaryCanonicalKernelTrajectory.lean:109
BanditRLProof.UCB.canonicalKernelTrajectoryReward definition UCB BanditRLProof.Algorithms.UCBRealStationaryCanonicalKernelTrajectory Compiled BanditRLProof/Algorithms/UCBRealStationaryCanonicalKernelTrajectory.lean:114
BanditRLProof.UCB.realStationaryUCBSequence_canonicalKernelTrajectory theorem UCB BanditRLProof.Algorithms.UCBRealStationaryCanonicalKernelTrajectory Compiled BanditRLProof/Algorithms/UCBRealStationaryCanonicalKernelTrajectory.lean:122
BanditRLProof.UCB.canonicalKernelTrajectoryArmwiseBoundedFiniteArmExpectedRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBRealStationaryCanonicalKernelTrajectory Compiled BanditRLProof/Algorithms/UCBRealStationaryCanonicalKernelTrajectory.lean:168
BanditRLProof.UCB.canonicalKernelTrajectoryArmwiseBoundedFiniteArmExpectedAverageRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBRealStationaryCanonicalKernelTrajectory Compiled BanditRLProof/Algorithms/UCBRealStationaryCanonicalKernelTrajectory.lean:218
BanditRLProof.UCB.canonicalRealUCBHistorySelector definition UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:20
BanditRLProof.UCB.canonicalRealUCBPolicyKernel definition UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:26
BanditRLProof.UCB.measurable_canonicalRealUCBHistorySelector theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:34
BanditRLProof.UCB.canonicalRealUCBPolicyKernel_apply theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:41
BanditRLProof.UCB.canonicalArmStreamHistoryAlgorithm_initialAction_eq_dirac theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:49
BanditRLProof.UCB.canonicalArmStreamHistoryAlgorithm_policy_ae_eq_explicitPolicyKernel theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:61
BanditRLProof.UCB.canonicalKernelTrajectory_finitePairHistory_map_eq_armStream theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:95
BanditRLProof.UCB.canonicalKernelTrajectoryAction_condDistrib_ae_eq_explicitPolicyKernel theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:137
BanditRLProof.UCB.canonicalKernelTrajectoryAction_zero_ae_eq_initializationArm theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:166
BanditRLProof.UCB.canonicalKernelTrajectoryAction_succ_ae_eq_realHistoryNextArm theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:198
BanditRLProof.UCB.canonicalKernelTrajectoryAction_succ_ae_eq_realHistoryNextArm_all theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:255
BanditRLProof.UCB.canonicalKernelTrajectoryAction_follows_realHistoryNextArm_ae theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:272
BanditRLProof.UCB.canonicalKernelTrajectoryArmwiseBoundedFiniteArmExpectedAverageRegret_tendsto_zero_and_explicitPolicy theorem UCB BanditRLProof.Algorithms.UCBRealStationaryExplicitPolicy Compiled BanditRLProof/Algorithms/UCBRealStationaryExplicitPolicy.lean:299
BanditRLProof.UCB.realStationaryExpectedRegret definition UCB BanditRLProof.Algorithms.UCBRealStationaryFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBRealStationaryFiniteArmRewardLaws.lean:20
BanditRLProof.UCB.realStationaryExpectedRegret_eq_armStreamExpectedRegret theorem UCB BanditRLProof.Algorithms.UCBRealStationaryFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBRealStationaryFiniteArmRewardLaws.lean:30
BanditRLProof.UCB.realStationaryExpectedAverageRegret definition UCB BanditRLProof.Algorithms.UCBRealStationaryFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBRealStationaryFiniteArmRewardLaws.lean:54
BanditRLProof.UCB.realStationaryExpectedAverageRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBRealStationaryFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBRealStationaryFiniteArmRewardLaws.lean:64
BanditRLProof.UCB.realStationaryArmwiseBoundedFiniteArmExpectedRegret definition UCB BanditRLProof.Algorithms.UCBRealStationaryFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBRealStationaryFiniteArmRewardLaws.lean:89
BanditRLProof.UCB.realStationaryArmwiseBoundedFiniteArmModelCoefficient definition UCB BanditRLProof.Algorithms.UCBRealStationaryFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBRealStationaryFiniteArmRewardLaws.lean:96
BanditRLProof.UCB.realStationaryArmwiseBoundedFiniteArmExpectedRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBRealStationaryFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBRealStationaryFiniteArmRewardLaws.lean:108
BanditRLProof.UCB.realStationaryArmwiseBoundedFiniteArmExpectedAverageRegret definition UCB BanditRLProof.Algorithms.UCBRealStationaryFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBRealStationaryFiniteArmRewardLaws.lean:156
BanditRLProof.UCB.realStationaryArmwiseBoundedFiniteArmExpectedAverageRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBRealStationaryFiniteArmRewardLaws Compiled BanditRLProof/Algorithms/UCBRealStationaryFiniteArmRewardLaws.lean:168
BanditRLProof.UCB.condDistrib_comp_measurePreserving theorem UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:27
BanditRLProof.UCB.measurePreservingArmStreamAction definition UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:54
BanditRLProof.UCB.measurePreservingArmStreamReward definition UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:62
BanditRLProof.UCB.realStationaryUCBSequence_comp_measurePreserving_armStream theorem UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:73
BanditRLProof.UCB.productNoiseArmStreamAction definition UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:149
BanditRLProof.UCB.productNoiseArmStreamReward definition UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:156
BanditRLProof.UCB.realStationaryUCBSequence_productNoise_armStream theorem UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:163
BanditRLProof.UCB.finiteArmProductNoiseMeasure definition UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:177
BanditRLProof.UCB.productNoiseArmwiseBoundedFiniteArmExpectedRegret_nonneg_and_le theorem UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:191
BanditRLProof.UCB.productNoiseArmwiseBoundedFiniteArmExpectedAverageRegret_tendsto_zero theorem UCB BanditRLProof.Algorithms.UCBRealStationaryMeasurePreservingSource Compiled BanditRLProof/Algorithms/UCBRealStationaryMeasurePreservingSource.lean:240
BanditRLProof.UCB.canonicalKernelTrajectory_historyAction_map_eq_armStream theorem UCB BanditRLProof.Algorithms.UCBRealStationarySelectedRewardConsistency Compiled BanditRLProof/Algorithms/UCBRealStationarySelectedRewardConsistency.lean:22
BanditRLProof.UCB.canonicalKernelTrajectoryReward_zero_condDistrib_ae_eq_nu theorem UCB BanditRLProof.Algorithms.UCBRealStationarySelectedRewardConsistency Compiled BanditRLProof/Algorithms/UCBRealStationarySelectedRewardConsistency.lean:93
BanditRLProof.UCB.canonicalKernelTrajectoryReward_succ_condDistrib_ae_eq_nu theorem UCB BanditRLProof.Algorithms.UCBRealStationarySelectedRewardConsistency Compiled BanditRLProof/Algorithms/UCBRealStationarySelectedRewardConsistency.lean:126
BanditRLProof.UCB.canonicalKernelTrajectoryArmwiseBoundedFiniteArmExpectedAverageRegret_tendsto_zero_and_explicitPolicy_and_selectedRewardLaws theorem UCB BanditRLProof.Algorithms.UCBRealStationarySelectedRewardConsistency Compiled BanditRLProof/Algorithms/UCBRealStationarySelectedRewardConsistency.lean:161
BanditRLProof.HarnessProfile inductive type Frontier BanditRLProof.Automation Compiled BanditRLProof/Automation.lean:13
BanditRLProof.AgentRole inductive type Frontier BanditRLProof.Automation Compiled BanditRLProof/Automation.lean:17
BanditRLProof.TaskKind inductive type Frontier BanditRLProof.Automation Compiled BanditRLProof/Automation.lean:24
BanditRLProof.TaskStatus inductive type Frontier BanditRLProof.Automation Compiled BanditRLProof/Automation.lean:32
BanditRLProof.ArtifactSpec structure Frontier BanditRLProof.Automation Compiled BanditRLProof/Automation.lean:40
BanditRLProof.AcceptanceGate structure Frontier BanditRLProof.Automation Compiled BanditRLProof/Automation.lean:46
BanditRLProof.HarnessTask structure Frontier BanditRLProof.Automation Compiled BanditRLProof/Automation.lean:53
BanditRLProof.defaultLeanGate definition Frontier BanditRLProof.Automation Compiled BanditRLProof/Automation.lean:63
BanditRLProof.defaultHarnessProfile definition Frontier BanditRLProof.Automation Compiled BanditRLProof/Automation.lean:69
BanditRLProof.Concentration.intervalVarianceProxy_pos_of_lt theorem Probability layer BanditRLProof.BoundedRewardKernelLaw Compiled BanditRLProof/BoundedRewardKernelLaw.lean:19
BanditRLProof.RewardKernel.centeredRewardKernelLaw_of_hasSubgaussianMGF definition Probability layer BanditRLProof.BoundedRewardKernelLaw Compiled BanditRLProof/BoundedRewardKernelLaw.lean:37
BanditRLProof.RewardKernel.boundedCenteredRewardKernelLaw definition Probability layer BanditRLProof.BoundedRewardKernelLaw Compiled BanditRLProof/BoundedRewardKernelLaw.lean:82
BanditRLProof.Budget.budgetExhaustionTime definition Frontier BanditRLProof.BudgetStoppingTime Compiled BanditRLProof/BudgetStoppingTime.lean:24
BanditRLProof.Budget.isStoppingTime_budgetExhaustionTime_of_adapted theorem Frontier BanditRLProof.BudgetStoppingTime Compiled BanditRLProof/BudgetStoppingTime.lean:36
BanditRLProof.Budget.measurableSet_budgetExhaustionTime_le_of_adapted theorem Frontier BanditRLProof.BudgetStoppingTime Compiled BanditRLProof/BudgetStoppingTime.lean:49
BanditRLProof.Concentration.geometricConfidenceShare definition Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:15
BanditRLProof.Concentration.geometricConfidenceShare_pos theorem Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:20
BanditRLProof.Concentration.tsum_ofReal_geometricConfidenceShare theorem Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:28
BanditRLProof.Concentration.telescopingConfidenceWeight definition Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:57
BanditRLProof.Concentration.telescopingConfidenceWeight_eq_sub theorem Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:61
BanditRLProof.Concentration.sum_range_telescopingConfidenceWeight theorem Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:70
BanditRLProof.Concentration.telescopingConfidenceWeight_nonneg theorem Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:79
BanditRLProof.Concentration.hasSum_telescopingConfidenceWeight theorem Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:85
BanditRLProof.Concentration.telescopingConfidenceShare definition Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:103
BanditRLProof.Concentration.telescopingConfidenceShare_eq_div theorem Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:108
BanditRLProof.Concentration.telescopingConfidenceShare_pos theorem Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:116
BanditRLProof.Concentration.tsum_ofReal_telescopingConfidenceShare theorem Probability layer BanditRLProof.ConcentrationConfidenceSchedule Compiled BanditRLProof/ConcentrationConfidenceSchedule.lean:124
BanditRLProof.Concentration.measure_iUnion_iUnion_fintype_le_tsum_of_uniform theorem Probability layer BanditRLProof.ConcentrationFintypeGeometricAllTime Compiled BanditRLProof/ConcentrationFintypeGeometricAllTime.lean:24
BanditRLProof.Concentration.measure_iUnion_iUnion_fintype_le_delta_of_geometricConfidenceShare theorem Probability layer BanditRLProof.ConcentrationFintypeGeometricAllTime Compiled BanditRLProof/ConcentrationFintypeGeometricAllTime.lean:50
BanditRLProof.Concentration.measure_iUnion_iUnion_fintype_le_delta_of_telescopingConfidenceShare theorem Probability layer BanditRLProof.ConcentrationFintypeTelescopingAllTime Compiled BanditRLProof/ConcentrationFintypeTelescopingAllTime.lean:22
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt structure Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:25
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.ae_integrable_exp_mul lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:32
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.ae_forall_integrable_exp_mul lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:36
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.congr lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:45
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.congr_iff lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:57
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.memLp_exp_mul lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:61
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.zero_kernel lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:77
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.zero_measure lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:83
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.prodMkLeft_compProd lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:90
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.integrable_exp_add_compProd lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:105
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.add_compProd theorem Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:127
BanditRLProof.Concentration.Kernel.HasMGFUpperBoundAt.add_comp lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:156
BanditRLProof.Concentration.HasMGFUpperBoundAt structure Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:172
BanditRLProof.Concentration.hasMGFUpperBoundAt_iff_kernel lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:177
BanditRLProof.Concentration.HasMGFUpperBoundAt.of_map lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:186
BanditRLProof.Concentration.HasMGFUpperBoundAt.id_map_iff lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:197
BanditRLProof.Concentration.HasMGFUpperBoundAt.compensated theorem Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:210
BanditRLProof.Concentration.HasCondMGFUpperBoundAt definition Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:239
BanditRLProof.Concentration.HasMGFUpperBoundAt.trim lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:246
BanditRLProof.Concentration.HasMGFUpperBoundAt.add_of_hasCondMGFUpperBoundAt theorem Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:256
BanditRLProof.Concentration.HasMGFUpperBoundAt.measure_ge_le_exp_add lemma Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:276
BanditRLProof.Concentration.HasMGFUpperBoundAt.sum_of_hasCondMGFUpperBoundAt theorem Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:290
BanditRLProof.Concentration.measure_sum_ge_le_of_hasCondMGFUpperBoundAt theorem Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:316
BanditRLProof.Concentration.measure_sum_ge_inter_sum_le_of_compensated_hasCondMGFUpperBoundAt theorem Probability layer BanditRLProof.ConcentrationFixedMGF Compiled BanditRLProof/ConcentrationFixedMGF.lean:333
BanditRLProof.Concentration.exists_tilt_quadratic_fixedMGF_exponent_le_neg theorem Probability layer BanditRLProof.ConcentrationQuadraticFixedMGF Compiled BanditRLProof/ConcentrationQuadraticFixedMGF.lean:20
BanditRLProof.Concentration.quadraticFixedMGFRadius definition Probability layer BanditRLProof.ConcentrationQuadraticFixedMGF Compiled BanditRLProof/ConcentrationQuadraticFixedMGF.lean:106
BanditRLProof.Concentration.measure_deviation_ge_inter_variance_le_delta_of_fixedTilt_quadratic_tail theorem Probability layer BanditRLProof.ConcentrationQuadraticFixedMGF Compiled BanditRLProof/ConcentrationQuadraticFixedMGF.lean:113
BanditRLProof.Concentration.quadraticFixedMGFMaximalRadius definition Probability layer BanditRLProof.ConcentrationQuadraticMaximal Compiled BanditRLProof/ConcentrationQuadraticMaximal.lean:19
BanditRLProof.Concentration.measure_biUnion_deviation_ge_inter_variance_le_delta_of_fixedTilt_quadratic_tail theorem Probability layer BanditRLProof.ConcentrationQuadraticMaximal Compiled BanditRLProof/ConcentrationQuadraticMaximal.lean:27
BanditRLProof.Concentration.quadraticFixedMGFScheduledRadius definition Probability layer BanditRLProof.ConcentrationQuadraticScheduled Compiled BanditRLProof/ConcentrationQuadraticScheduled.lean:20
BanditRLProof.Concentration.measure_iUnion_scheduled_deviation_ge_inter_variance_le_tsum_of_fixedTilt_quadratic_tail theorem Probability layer BanditRLProof.ConcentrationQuadraticScheduled Compiled BanditRLProof/ConcentrationQuadraticScheduled.lean:29
BanditRLProof.Concentration.measure_iUnion_scheduled_deviation_ge_inter_variance_le_delta_of_fixedTilt_quadratic_tail theorem Probability layer BanditRLProof.ConcentrationQuadraticScheduled Compiled BanditRLProof/ConcentrationQuadraticScheduled.lean:78
ProbabilityTheory.HasCondSubgaussianMGF.of_measurableSpace_eq theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:17
ProbabilityTheory.HasCondSubgaussianMGF.integrable theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:37
ProbabilityTheory.HasCondSubgaussianMGF.indicator theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:73
ProbabilityTheory.HasCondSubgaussianMGF.indicator_compensated_hasCondMGFUpperBoundAt theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:171
BanditRLProof.Concentration.intervalVarianceProxy definition Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:332
BanditRLProof.Concentration.boundedCentered_hasSubgaussianMGF_of_mem_Icc_integral_eq theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:343
BanditRLProof.Concentration.integral_abs_le_two_mul_sqrt_mul_exp_half_of_hasSubgaussianMGF theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:372
BanditRLProof.Concentration.integral_sq_le_four_mul_proxy_mul_exp_half_of_hasSubgaussianMGF theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:456
BanditRLProof.Concentration.subGaussian_sum_tail_of_iIndepFun theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:545
BanditRLProof.Concentration.subGaussian_sum_tail_ennreal_of_iIndepFun theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:567
BanditRLProof.Concentration.condSubGaussian_sum_tail_of_stronglyAdapted theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:596
BanditRLProof.Concentration.condSubGaussian_sum_tail_ennreal_of_stronglyAdapted theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:623
BanditRLProof.Concentration.subGaussian_sum_abs_tail_ennreal_of_iIndepFun theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:655
BanditRLProof.Concentration.condSubGaussian_sum_abs_tail_ennreal_of_stronglyAdapted theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:729
BanditRLProof.Concentration.subGaussianSumConfidenceRadius definition Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:804
BanditRLProof.Concentration.subGaussianSumConfidenceRadius_nonneg theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:808
BanditRLProof.Concentration.subGaussianSumConfidenceRadius_sq theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:813
BanditRLProof.Concentration.two_mul_exp_neg_subGaussianSumConfidenceRadius_sq_div_eq_delta theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:825
BanditRLProof.Concentration.subGaussian_sum_abs_tail_ennreal_delta_of_iIndepFun theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:849
BanditRLProof.Concentration.condSubGaussian_sum_abs_tail_ennreal_delta_of_stronglyAdapted theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:880
BanditRLProof.Concentration.subGaussianAverageConfidenceRadius definition Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:915
BanditRLProof.Concentration.subGaussianAverageConfidenceRadius_nonneg theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:919
BanditRLProof.Concentration.measure_average_abs_tail_le_of_measure_sum_abs_tail theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:930
BanditRLProof.Concentration.measure_randomCount_average_abs_tail_le_of_measure_sum_abs_tail theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:962
BanditRLProof.Concentration.measure_positive_randomCount_event_le_sum_exactCount theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:989
BanditRLProof.Concentration.measure_positive_randomCount_event_le_of_exactCount_uniform theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:1026
BanditRLProof.Concentration.subGaussian_average_abs_tail_ennreal_delta_of_iIndepFun theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:1065
BanditRLProof.Concentration.condSubGaussian_average_abs_tail_ennreal_delta_of_stronglyAdapted theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:1101
BanditRLProof.Concentration.condSubGaussian_indicator_sum_tail_predictableVariance_fixedTilt theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:1137
BanditRLProof.Concentration.subGaussianPredictableVarianceRadius definition Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:1219
BanditRLProof.Concentration.condSubGaussian_indicator_sum_abs_tail_predictableVariance_delta theorem Probability layer BanditRLProof.ConcentrationSubGaussian Compiled BanditRLProof/ConcentrationSubGaussian.lean:1227
BanditRLProof.Concentration.variance_chebyshev_tail theorem Probability layer BanditRLProof.ConcentrationVariance Compiled BanditRLProof/ConcentrationVariance.lean:26
BanditRLProof.Concentration.evariance_chebyshev_tail theorem Probability layer BanditRLProof.ConcentrationVariance Compiled BanditRLProof/ConcentrationVariance.lean:42
BanditRLProof.Concentration.variance_sum_of_pairwise_indep theorem Probability layer BanditRLProof.ConcentrationVariance Compiled BanditRLProof/ConcentrationVariance.lean:59
BanditRLProof.ConditionalExpectationReward.condExp_eq_zero_of_condExpKernel_integral_eq_zero theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:36
BanditRLProof.ConditionalExpectationReward.hasSubgaussianMGF_mono_varianceProxy theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:80
BanditRLProof.ConditionalExpectationReward.condExpKernel_map_eq_deterministic_of_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:109
BanditRLProof.ConditionalExpectationReward.condExpKernel_map_eq_dirac_of_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:145
BanditRLProof.ConditionalExpectationReward.condExpKernel_map_eq_of_condDistrib_ae_eq_countable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:177
BanditRLProof.ConditionalExpectationReward.condExpKernel_map_eq_of_condDistrib_ae_eq_countable_trim theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:251
BanditRLProof.ConditionalExpectationReward.condExpKernel_map_eq_of_condDistrib_ae_eq_real_trim theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:330
BanditRLProof.ConditionalExpectationReward.eventuallyEq_const_of_map_eq_dirac theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:476
BanditRLProof.ConditionalExpectationReward.pair_map_eq_map_prod_mk_of_action_ae_eq_const_reward_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:510
BanditRLProof.ConditionalExpectationReward.condExpKernel_pair_map_eq_map_prod_mk_of_action_ae_reward_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:564
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_selectedMeasure_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:623
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_selectedMeasure_condExpKernel_map_trajMeasure_trim theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:706
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_identDistrib_trajMeasure_of_condDistrib theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:804
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_selectedMeasure_condExpKernel_map_of_identDistrib_trajMeasure_trim theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:865
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1008
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_action_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1091
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_actionMarginal_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1189
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_selectedAction_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1274
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_selectedAction_condExpKernel_ae_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1357
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_extend_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1440
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_reward_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1582
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_selectedMeasure_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1664
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_selectedMeasure_finitePairHistoryOfTrace_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1735
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_selectedMeasure_rewardHistoryOfTrace_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1808
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_condExpKernel_map_trajMeasure_of_selectedAction_ae_selectedMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:1919
BanditRLProof.ConditionalExpectationReward.hasCondSubgaussianMGF_of_condExpKernel_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2037
BanditRLProof.ConditionalExpectationReward.hasCondSubgaussianMGF_centered_of_condExpKernel_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2120
BanditRLProof.ConditionalExpectationReward.hasCondSubgaussianMGF_congr_measurableSpace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2197
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_condExpKernel_integral_eq_zero theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2220
BanditRLProof.ConditionalExpectationReward.condExp_eq_zero_of_condExpKernel_integral_eq_historyStepKernel_centeredReward theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2266
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_historyStepKernelFamily_condExpKernel_integral_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2324
BanditRLProof.ConditionalExpectationReward.condExp_eq_zero_of_condExpKernel_map_eq_historyStepKernel_centeredReward theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2417
BanditRLProof.ConditionalExpectationReward.hasCondSubgaussianMGF_of_condExpKernel_map_eq_historyStepKernel_centeredReward theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2538
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_historyStepKernelFamily_condExpKernel_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2708
BanditRLProof.ConditionalExpectationReward.condExpKernel_event_real_eq_indicator_of_measurableSet theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2815
BanditRLProof.ConditionalExpectationReward.condExpKernel_ae_eq_const_of_countable_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2853
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_prefix_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:2929
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_finitePairHistoryOfTrace_condExpKernel_map_trajMeasure theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3112
BanditRLProof.ConditionalExpectationReward.action_condExpKernel_ae_eq_policy_of_measurable_of_policy_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3210
BanditRLProof.ConditionalExpectationReward.action_condExpKernel_ae_eq_policy_of_pairHistory_measurable_of_action_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3267
BanditRLProof.ConditionalExpectationReward.action_condExpKernel_ae_eq_policy_historyFiltrationSucc_finitePairHistoryOfTrace_of_action_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3337
BanditRLProof.ConditionalExpectationReward.action_condExpKernel_ae_eq_policy_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionTraceSucc theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3431
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_policy_of_action_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3507
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_actual_action_of_pair_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3564
BanditRLProof.ConditionalExpectationReward.random_pair_condExpKernel_map_eq_actual_action_of_generatedActionTraceSucc_reward_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3651
BanditRLProof.ConditionalExpectationReward.pair_condExpKernel_map_eq_frozen_actual_action_of_generatedActionTraceSucc_random_pair_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3791
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionTraceSucc_random_pair_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:3942
BanditRLProof.ConditionalExpectationReward.finiteRewardHistory_condExpKernel_frozen_of_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4059
BanditRLProof.ConditionalExpectationReward.finiteRewardHistory_condExpKernel_frozen_of_coordinate_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4093
BanditRLProof.ConditionalExpectationReward.finiteRewardHistory_condExpKernel_frozen_historyFiltrationSucc theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4134
BanditRLProof.ConditionalExpectationReward.finitePairHistory_condExpKernel_frozen_of_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4181
BanditRLProof.ConditionalExpectationReward.finitePairHistory_condExpKernel_frozen_of_coordinate_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4216
BanditRLProof.ConditionalExpectationReward.finitePairHistory_condExpKernel_frozen_historyFiltrationSucc theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4265
BanditRLProof.ConditionalExpectationReward.finitePairHistory_succ_ae_eq_extend_of_pairHistory_frozen theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4320
BanditRLProof.ConditionalExpectationReward.finitePairHistory_succ_condExpKernel_ae_eq_extend_historyFiltrationSucc theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4361
BanditRLProof.ConditionalExpectationReward.finitePairHistory_succ_condExpKernel_map_eq_extend_historyFiltrationSucc theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4420
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_frozenPast_ae_of_history_frozen theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4476
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_historyStepKernelFamily_condExpKernel_map_eq_of_coordinate_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4525
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_historyStepKernelFamily_condExpKernel_map_eq_historyFiltrationSucc theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4678
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_historyStepKernelFamily_condExpKernel_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4789
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_historyStepKernelFamily_condExpKernel_map_eq_of_coordinate_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:4890
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_historyStepKernelFamily_condExpKernel_map_eq_historyFiltrationSucc theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:5028
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_of_coordinate_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:5125
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:5289
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_projected theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:5411
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_projected_of_context_state_measurable theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:5531
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:5643
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_of_actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:5749
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_actual_action_of_actionRewardHistoryStepKernelFamily_pair_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:5958
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_actual_action_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:6066
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_actual_action_of_generatedActionTraceSucc_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:6193
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_actual_action_of_actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:6301
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_actual_action_of_generatedActionTraceSucc_actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:6489
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:6599
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_of_action_ae_eq_policy_reward_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:6856
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionTraceSucc_reward_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:6981
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_extend_map_eq_of_actionRewardHistoryStepKernelFamily_pair_map_eq theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:7134
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_extend_map_eq_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:7256
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_extend_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionTraceSucc_reward_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:7372
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_of_extend_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:7538
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_actual_action_of_actionRewardPartialTrajectoryKernel_extend_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:7663
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_actual_action_of_generatedActionTraceSucc_actionRewardPartialTrajectoryKernel_extend_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:7809
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionTraceSucc_reward_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:7922
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardPartialTrajectoryKernel_extend_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:8070
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_reward_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:8228
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionTraceSucc_pair_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:8376
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_pair_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:8510
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionTraceSucc_random_pair_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:8660
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_random_pair_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalExpectationReward Compiled BanditRLProof/ConditionalExpectationReward.lean:8837
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_centeredReward_succ_condExp_eq_zero_trajMeasure_of_condSubgaussian theorem Probability layer BanditRLProof.ConditionalRewardFoundation Compiled BanditRLProof/ConditionalRewardFoundation.lean:28
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_conditionalRewardFoundation_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardFoundation Compiled BanditRLProof/ConditionalRewardFoundation.lean:139
BanditRLProof.ConditionalExpectationReward.eventually_ae_trim_of_eq_measurableSpace theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:25
BanditRLProof.ConditionalExpectationReward.generatedActionFromRewardHistory definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:39
BanditRLProof.ConditionalExpectationReward.generatedActionFromRewardHistory_measurable theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:56
BanditRLProof.ConditionalExpectationReward.comap_finitePairHistoryOfTrace_generatedActionFromRewardHistory_eq_comap_finiteRewardHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:92
BanditRLProof.ConditionalExpectationReward.historyFiltrationSucc_generatedActionFromRewardHistory_eq_comap_finiteRewardHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:241
BanditRLProof.ConditionalExpectationReward.generatedActionFromRewardHistory_succ_measurable_historyFiltrationSucc theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:286
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_selectedMeasure_condExpKernel_map_trajMeasure_generatedActionFromRewardHistory_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:343
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_selectedMeasure_condExpKernel_map_trajMeasure_generatedActionFromRewardHistory_finitePairHistoryOfTrace_trim theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:420
BanditRLProof.ConditionalExpectationReward.GeneratedActionPartialTrajectoryPairLawSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:578
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_partialTrajectoryPairLawSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:657
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_partialTrajectoryKernel_extend_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:737
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_actionRewardHistoryStepKernelFamily_pair_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:847
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_action_ae_eq_policy_reward_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:959
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:1155
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_reward_map_eq_selected_policy theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:1273
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_reward_map_eq_actual_action definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:1411
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_reward_map_eq_actual_action theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:1500
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_finitePairHistory_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:1638
BanditRLProof.ConditionalExpectationReward.GeneratedActionSelectedRewardFinitePairHistoryLawSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:1725
BanditRLProof.ConditionalExpectationReward.generatedActionSelectedRewardFinitePairHistoryLawSource_of_comap_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:1796
BanditRLProof.ConditionalExpectationReward.generatedActionSelectedRewardFinitePairHistoryLawSource_of_comap_trim_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:1970
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_generatedActionSelectedRewardFinitePairHistoryLawSource_trajMeasure definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2144
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_generatedActionSelectedRewardFinitePairHistoryLawSource_of_identDistrib_trajMeasure definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2211
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_generatedActionSelectedRewardFinitePairHistoryLawSource_of_condDistrib definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2297
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_selectedRewardFinitePairHistoryLawSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2353
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_generatedActionPartialTrajectoryPairLawSource_of_condDistrib definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2394
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_generatedActionPartialTrajectoryPairLawSource_trajMeasure definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2447
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2507
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_centeredReward_succ_condExp_eq_zero_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2599
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_centeredReward_succ_hasCondSubgaussianMGF_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2719
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_partialTrajectoryPairLawSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:2956
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_centeredReward_succ_hasCondSubgaussianMGF_of_condDistrib theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:3164
BanditRLProof.ConditionalExpectationReward.generatedActionFromRewardHistory_centeredRewardSuccProcess_stronglyAdapted theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:3265
BanditRLProof.ConditionalExpectationReward.generatedActionFromRewardHistory_armMaskedCenteredRewardSuccProcess_stronglyAdapted theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:3428
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_centeredRewardSuccProcess_sum_tail_ennreal_of_condDistrib theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:3541
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_centeredRewardSuccProcess_sum_tail_ennreal_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:3676
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_centeredRewardSuccProcess_average_tail_ennreal_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:3808
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_comap_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:3924
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_comap_trim_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4016
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_selectedRewardFinitePairHistoryLawSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4160
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_comap_reward_map_eq_selected_policy theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4265
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_comap_trim_reward_map_eq_selected_policy theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4410
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairMapSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4608
BanditRLProof.ConditionalExpectationReward.GeneratedActionActualRewardMapSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4661
BanditRLProof.ConditionalExpectationReward.GeneratedActionDefinitionalActualRewardMapSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4713
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4772
BanditRLProof.ConditionalExpectationReward.generatedActionSelectedRewardFinitePairHistoryLawSource_of_definitionalActualRewardMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4841
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_partialTrajectoryKernel_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4881
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_partialTrajectoryPairLawSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:4988
BanditRLProof.ConditionalExpectationReward.generatedActionSelectedRewardFinitePairHistoryLawSource_of_partialTrajectoryPairLawSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:5032
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_partialTrajectoryKernel_extend_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:5085
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_actionRewardHistoryStepKernelFamily_pair_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:5202
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairDefinitionalMapSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:5306
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalMapSource_of_actionRewardPartialTrajectoryKernel_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:5372
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalMapSource_of_partialTrajectoryPairLawSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:5581
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalMapSource_of_actionRewardPartialTrajectoryKernel_extend_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:5625
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalMapSource_of_actionRewardHistoryStepKernelFamily_pair_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:5741
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalMapSource_of_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:5894
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_definitionalMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6082
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_actionRewardHistoryStepKernelFamily_pair_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6121
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_actionRewardPartialTrajectoryKernel_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6245
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_actionRewardPartialTrajectoryKernel_extend_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6344
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_definitionalActualRewardMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6442
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_partialTrajectoryPairLawSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6479
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_partialTrajectoryKernel_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6535
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_partialTrajectoryKernel_extend_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6627
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_actionRewardHistoryStepKernelFamily_pair_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6719
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6808
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_generatedActionActualRewardMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:6937
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_generatedActionDefinitionalActualRewardMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7049
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_randomPairDefinitionalMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7109
BanditRLProof.ConditionalExpectationReward.reward_condExpKernel_map_eq_selected_policy_of_generatedActionRandomPairDefinitionalMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7179
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_randomPairDefinitionalMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7255
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairCenteredSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7308
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairDefinitionalCenteredSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7356
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_of_generatedActionRandomPairDefinitionalCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7396
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairCenteredSource_of_definitionalCenteredSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7433
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_randomPairDefinitionalCenteredSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7485
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_randomPairDefinitionalCenteredSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7531
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairDefinitionalCenteredSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7572
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_randomPairCenteredSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7630
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairCenteredSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7667
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairBoundedCenteredSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7714
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairRawMeanBoundedSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7777
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairRawBoundMeanBoundedSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7849
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairRawBoundMeasurableMeanBoundedSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7917
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairRawBoundMeasurableMeanRangeBoundedSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:7976
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairRawRangeMeasurableMeanRangeBoundedSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8026
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8073
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8117
BanditRLProof.ConditionalExpectationReward.GeneratedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource structure Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8152
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8188
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_historyVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8225
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8260
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_actionRewardPartialTrajectoryKernel_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8302
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_partialTrajectoryPairLawSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8416
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_comap_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8484
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_comap_trim_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8606
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_actionRewardPartialTrajectoryKernel_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8779
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_partialTrajectoryPairLawSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8904
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_comap_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:8978
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_comap_trim_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:9106
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_actionRewardPartialTrajectoryKernel_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:9285
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_partialTrajectoryPairLawSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:9411
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_comap_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:9487
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_comap_trim_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:9616
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_actionRewardPartialTrajectoryKernel_extend_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:9796
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_actionRewardPartialTrajectoryKernel_extend_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:9914
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_actionRewardPartialTrajectoryKernel_extend_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10042
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_actionRewardHistoryStepKernelFamily_pair_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10172
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_actionRewardHistoryStepKernelFamily_pair_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10284
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_actionRewardHistoryStepKernelFamily_pair_map_eq definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10406
BanditRLProof.ConditionalExpectationReward.rawReward_succ_aemeasurable_of_measurable_reward theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10525
BanditRLProof.ConditionalExpectationReward.selectedMean_succ_aemeasurable_of_measurable_mean theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10542
BanditRLProof.ConditionalExpectationReward.selectedMean_succ_bound_of_mean_range_bound theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10609
BanditRLProof.ConditionalExpectationReward.rawReward_succ_bound_of_reward_range_bound theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10649
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_of_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10677
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_historyStepKernelFamily_condExpKernel_map_eq_of_coordinate_measurable_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10847
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_historyStepKernelFamily_condExpKernel_map_eq_historyFiltrationSucc_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:10965
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_of_coordinate_measurable_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:11087
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:11232
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_projected_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:11359
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_projected_of_context_state_measurable_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:11486
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:11606
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardPartialTrajectoryKernel_extend_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:11744
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:11885
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12019
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_action_ae_eq_policy_reward_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12138
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_reward_map_eq_selected_policy_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12334
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairRawMeanBoundedSource_of_rawBoundMeanBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12491
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairRawBoundMeanBoundedSource_of_rawBoundMeasurableMeanBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12534
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairRawBoundMeasurableMeanBoundedSource_of_rawBoundMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12578
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairRawBoundMeasurableMeanRangeBoundedSource_of_rawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12623
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairRawRangeMeasurableMeanRangeBoundedSource_of_definitionalRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12667
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_definitionalRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12722
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_aemeasurable_of_generatedActionRandomPairRawMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12766
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_bound_of_generatedActionRandomPairRawMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12810
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairBoundedCenteredSource_of_rawMeanBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12885
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_of_generatedActionRandomPairBoundedCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:12961
BanditRLProof.ConditionalExpectationReward.integrable_exp_mul_of_mem_Icc theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13006
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_exp_of_generatedActionRandomPairBoundedCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13043
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairCenteredSource_of_boundedCenteredSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13104
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_randomPairBoundedCenteredSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13162
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairBoundedCenteredSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13200
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_randomPairRawMeanBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13249
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairRawMeanBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13287
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_randomPairRawBoundMeanBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13336
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairRawBoundMeanBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13374
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_randomPairRawBoundMeasurableMeanBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13423
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairRawBoundMeasurableMeanBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13461
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_randomPairRawBoundMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13511
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairRawBoundMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13551
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_randomPairRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13602
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13642
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_randomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13694
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_randomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13739
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_randomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13805
BanditRLProof.ConditionalExpectationReward.generatedActionSelectedRewardFinitePairHistoryLawSource_of_randomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13853
BanditRLProof.ConditionalExpectationReward.generatedActionSelectedRewardFinitePairHistoryLawSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13911
BanditRLProof.ConditionalExpectationReward.generatedActionSelectedRewardFinitePairHistoryLawSource_of_historyVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:13960
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionActualRewardMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:14006
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionActualRewardMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:14100
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionActualRewardMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:14175
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_reward_map_eq_actual_action_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:14260
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:14393
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_actionRewardPartialTrajectoryKernel_extend_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:14551
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_pair_map_eq_actual_action_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:14710
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionTraceSucc_random_pair_map_eq_actual_action_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:14846
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionActualRewardMapSource_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:14981
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionDefinitionalActualRewardMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15088
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionDefinitionalActualRewardMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15190
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalMapSource_of_generatedActionDefinitionalActualRewardMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15299
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionDefinitionalActualRewardMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15349
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15445
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15539
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15614
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairMapSource_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15698
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairDefinitionalMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15783
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairDefinitionalMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15885
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairDefinitionalMapSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:15990
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairDefinitionalMapSource_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:16089
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_reward_map_eq_selected_policy_definitionalMapSource_rawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:16197
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:16328
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:16400
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:16474
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:16543
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairBoundedCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:16771
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairDefinitionalCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:16876
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairDefinitionalCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:16981
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairDefinitionalCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17089
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17175
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairBoundedCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17295
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairBoundedCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17385
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairBoundedCenteredSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17477
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_of_generatedActionRandomPairRawMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17554
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17631
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17725
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairRawMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17821
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_aemeasurable_of_generatedActionRandomPairRawBoundMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17902
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_bound_of_generatedActionRandomPairRawBoundMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:17981
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_of_generatedActionRandomPairRawBoundMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18062
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawBoundMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18141
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawBoundMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18237
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairRawBoundMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18335
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_aemeasurable_of_generatedActionRandomPairRawBoundMeasurableMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18418
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_bound_of_generatedActionRandomPairRawBoundMeasurableMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18497
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_of_generatedActionRandomPairRawBoundMeasurableMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18578
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawBoundMeasurableMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18657
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawBoundMeasurableMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18753
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairRawBoundMeasurableMeanBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18851
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_aemeasurable_of_generatedActionRandomPairRawBoundMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:18934
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_bound_of_generatedActionRandomPairRawBoundMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19013
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_of_generatedActionRandomPairRawBoundMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19094
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawBoundMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19173
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawBoundMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19269
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairRawBoundMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19367
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_aemeasurable_of_generatedActionRandomPairRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19450
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_bound_of_generatedActionRandomPairRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19529
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_of_generatedActionRandomPairRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19610
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19689
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19785
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19883
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_aemeasurable_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:19966
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_measurable_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20049
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_bound_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20137
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairBoundedCenteredSource_of_definitionalRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20218
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairCenteredSource_of_definitionalRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20309
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20381
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_integrable_exp_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20460
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalCenteredSource_of_definitionalRawRangeMeasurableMeanRangeBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20544
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalCenteredSource_of_historyVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20598
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairBoundedCenteredSource_of_historyVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20664
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairCenteredSource_of_historyVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20737
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_historyVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20813
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_historyVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20879
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_historyVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:20951
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_historyVarianceBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21022
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairMapSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21137
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21210
BanditRLProof.ConditionalExpectationReward.generatedActionPartialTrajectoryPairLawSource_of_historyVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21277
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_uniformVarianceBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21342
BanditRLProof.ConditionalExpectationReward.generatedActionDefinitionalActualRewardMapSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21457
BanditRLProof.ConditionalExpectationReward.generatedActionActualRewardMapSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21523
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairBoundedCenteredSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21595
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairCenteredSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21668
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalCenteredSource_of_uniformVarianceBoundedSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21745
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_pair_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21807
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:21922
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22039
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22136
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_centered_meas theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22256
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_variance_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22364
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_uniform_variance_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22479
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_history_variance_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22567
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22648
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22724
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22803
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_via_historyVarianceSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22886
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:22986
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardHistoryStepKernelFamily_pair_map_eq_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:23091
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardHistoryStepKernelFamily_pair_map_eq_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:23255
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardPartialTrajectoryKernel_map_eq_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:23427
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_partialTrajectoryPairLawSource_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:23595
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardPartialTrajectoryKernel_map_eq_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:23693
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_partialTrajectoryPairLawSource_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:23869
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardPartialTrajectoryKernel_map_eq_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:23971
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_partialTrajectoryPairLawSource_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:24140
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardPartialTrajectoryKernel_map_eq_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:24239
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_partialTrajectoryPairLawSource_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:24416
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardPartialTrajectoryKernel_extend_map_eq_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:24519
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardPartialTrajectoryKernel_extend_map_eq_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:24689
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardPartialTrajectoryKernel_extend_map_eq_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:24867
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardPartialTrajectoryKernel_extend_map_eq_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:25038
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardHistoryStepKernelFamily_pair_map_eq_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:25217
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_actionRewardHistoryStepKernelFamily_pair_map_eq_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:25382
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardPartialTrajectoryKernel_map_eq_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:25555
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_partialTrajectoryPairLawSource_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:25711
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_selectedRewardFinitePairHistoryLawSource_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:25802
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_selectedRewardFinitePairHistoryLawSource_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:25905
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_selectedRewardFinitePairHistoryLawSource_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:26016
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_selectedRewardFinitePairHistoryLawSource_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:26131
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_selectedRewardFinitePairHistoryLawSource_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:26243
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_via_selectedRewardFinitePairHistoryLawSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:26362
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_via_selectedRewardFinitePairHistoryLawSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:26457
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_via_selectedRewardFinitePairHistoryLawSource_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:26562
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_via_selectedRewardFinitePairHistoryLawSource theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:26672
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_via_selectedRewardFinitePairHistoryLawSource_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:26778
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_comap_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:26892
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_comap_trim_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:27034
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_comap_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:27230
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_comap_trim_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:27384
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_comap_trim_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:27591
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_comap_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:27799
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_comap_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:27955
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_comap_trim_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:28110
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_comap_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:28315
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_comap_trim_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:28471
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardPartialTrajectoryKernel_extend_map_eq_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:28680
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_actionRewardHistoryStepKernelFamily_pair_map_eq_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:28840
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_reward_map_eq_actual_action_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:29050
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:29252
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_condExp_eq_zero_of_generatedActionDefinitionalActualRewardMapSource_definitionalRawRangeMeasurableMeanRangeBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:29382
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_generatedActionDefinitionalActualRewardMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:29472
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_generatedActionDefinitionalActualRewardMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:29537
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionDefinitionalActualRewardMapSource_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:29612
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionDefinitionalActualRewardMapSource_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:29732
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_generatedActionDefinitionalActualRewardMapSource definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:29857
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionDefinitionalActualRewardMapSource_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:29933
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_generatedActionDefinitionalActualRewardMapSource_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:30054
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_reward_map_eq_actual_action definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:30179
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeBoundedSource_of_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:30361
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_actual_action_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:30498
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_reward_map_eq_actual_action definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:30709
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_actual_action_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:30896
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:31052
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_selected_policy_definitionalMapSource_rawRangeMeasurableMeanRangeUniformVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:31219
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_selected_policy_definitionalMapSource_rawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:31376
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_selected_policy_definitionalMapSource_rawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:31539
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_selected_policy_definitionalMapSource_rawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:31697
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeUniformVarianceBoundedSource_of_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:31859
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeUniformVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:32002
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_actual_action_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:32158
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_reward_map_eq_actual_action definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:32370
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_actual_action_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:32558
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:32716
BanditRLProof.ConditionalExpectationReward.generatedActionRandomPairDefinitionalRawRangeMeasurableMeanRangeHistoryVarianceBoundedSource_of_reward_map_eq_selected_policy definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:32883
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded_of_varianceCeiling_le theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33027
BanditRLProof.ConditionalExpectationReward.centeredRewardSuccProcess_sum_tail_ennreal_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33188
BanditRLProof.ConditionalExpectationReward.centeredRewardSuccProcess_sum_abs_tail_ennreal_delta_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33372
BanditRLProof.ConditionalExpectationReward.successorArmPullCount definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33553
BanditRLProof.ConditionalExpectationReward.successorArmPullCount_le_horizon theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33559
BanditRLProof.ConditionalExpectationReward.successorArmRewardSum definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33567
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMean definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33575
BanditRLProof.ConditionalExpectationReward.armMaskedCenteredRewardSuccProcess_sum_eq_successorArmRewardSum_sub_pullCount_mul theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33589
BanditRLProof.ConditionalExpectationReward.armMaskedVarianceSuccProcess_sum_eq_mul_successorArmPullCount theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33675
BanditRLProof.ConditionalExpectationReward.armMaskedCenteredRewardSuccProcess_sum_abs_tail_ennreal_delta_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33717
BanditRLProof.ConditionalExpectationReward.armMaskedCenteredRewardSuccProcess_sum_abs_tail_predictableVariance_ennreal_delta_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:33930
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMeanExactCountRadius definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34134
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMean_abs_tail_exact_pullCount_ennreal_delta_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34145
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMeanPeelingRadius definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34369
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMean_abs_tail_random_pullCount_ennreal_delta_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34383
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMeanFiniteArmTimeConfidenceShare definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34524
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMeanFiniteArmTimePeelingRadius definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34530
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMeanFiniteArmTimeBadEvent definition Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34541
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMean_simultaneous_finiteArmTime_abs_tail_ennreal_delta_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34564
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMean_abs_tail_ennreal_delta_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34725
BanditRLProof.ConditionalExpectationReward.centeredRewardSuccProcess_average_abs_tail_ennreal_delta_of_reward_map_eq_selected_policy_definitionalRawRangeMeasurableMeanRangeHistoryVarianceBounded theorem Probability layer BanditRLProof.ConditionalRewardLawSource Compiled BanditRLProof/ConditionalRewardLawSource.lean:34929
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMeanFintypeGeometricAllTimeBadEvent definition Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryGeometricAllTime Compiled BanditRLProof/ConditionalRewardPartialTrajectoryGeometricAllTime.lean:29
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_successorArmEmpiricalMean_simultaneous_fintype_geometricAllTime_abs_tail_ennreal_delta_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryGeometricAllTime Compiled BanditRLProof/ConditionalRewardPartialTrajectoryGeometricAllTime.lean:49
BanditRLProof.ConditionalExpectationReward.historyStepKernelFamily_actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_condDistrib theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryLaw.lean:17
BanditRLProof.ConditionalExpectationReward.actionRewardPartialTrajectoryKernel_map_eq_historyFiltrationSucc_finitePairHistoryOfTrace_of_pair_condDistrib theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryLaw.lean:112
BanditRLProof.ConditionalExpectationReward.centeredRewardSuccProcess_stronglyAdapted_historyFiltrationSucc theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryLaw.lean:322
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_pair_condDistrib_of_ae_variance theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryLaw.lean:456
BanditRLProof.ConditionalExpectationReward.centeredReward_succ_hasCondSubgaussianMGF_of_pair_condDistrib theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryLaw.lean:657
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_centeredRewardSuccProcess_sum_tail_ennreal_of_pair_condDistrib theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryLaw.lean:742
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_centeredRewardSuccProcess_sum_tail_ennreal_of_pair_condDistrib_on_horizon theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryLaw.lean:868
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_centeredRewardSuccProcess_sum_tail_ennreal_trajMeasure_on_horizon theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryLaw.lean:1003
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_action_succ_ae_eq_policy_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryMaskedLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryMaskedLaw.lean:30
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_policyArmMaskedCenteredRewardSuccProcess_sum_abs_tail_predictableVariance_ennreal_delta_trajMeasure_on_horizon theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryMaskedLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryMaskedLaw.lean:112
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_sampledArmMaskedCenteredRewardSuccProcess_sum_abs_tail_successorPullCount_ennreal_delta_trajMeasure_on_horizon theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryMaskedLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryMaskedLaw.lean:341
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_successorArmEmpiricalMean_abs_tail_exact_pullCount_ennreal_delta_trajMeasure_on_horizon theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryMaskedLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryMaskedLaw.lean:582
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_successorArmEmpiricalMean_abs_tail_random_pullCount_ennreal_delta_trajMeasure_on_horizon theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryMaskedLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryMaskedLaw.lean:817
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_successorArmEmpiricalMean_simultaneous_finiteArmTime_abs_tail_ennreal_delta_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryMaskedLaw Compiled BanditRLProof/ConditionalRewardPartialTrajectoryMaskedLaw.lean:956
BanditRLProof.ConditionalExpectationReward.successorArmEmpiricalMeanFintypeTelescopingAllTimeBadEvent definition Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryTelescopingAllTime Compiled BanditRLProof/ConditionalRewardPartialTrajectoryTelescopingAllTime.lean:29
BanditRLProof.ConditionalExpectationReward.actionRewardHistoryStepKernelFamily_successorArmEmpiricalMean_simultaneous_fintype_telescopingAllTime_abs_tail_ennreal_delta_trajMeasure theorem Probability layer BanditRLProof.ConditionalRewardPartialTrajectoryTelescopingAllTime Compiled BanditRLProof/ConditionalRewardPartialTrajectoryTelescopingAllTime.lean:49
BanditRLProof.ActionTrace abbreviation Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:17
BanditRLProof.RewardTrace abbreviation Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:20
BanditRLProof.pullCount definition Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:23
BanditRLProof.pullCount_zero theorem Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:27
BanditRLProof.pullCount_succ theorem Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:31
BanditRLProof.sumRewards definition Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:37
BanditRLProof.sumRewards_zero theorem Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:44
BanditRLProof.sumRewards_succ theorem Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:49
BanditRLProof.FiniteBanditModel structure Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:56
BanditRLProof.FiniteBanditModel.bestArm definition Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:63
BanditRLProof.FiniteBanditModel.bestMean definition Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:69
BanditRLProof.FiniteBanditModel.gap definition Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:73
BanditRLProof.FiniteBanditModel.gap_bestArm theorem Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:76
BanditRLProof.PolicySketch structure Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:83
BanditRLProof.CertificateStatus inductive type Foundations BanditRLProof.Core Compiled BanditRLProof/Core.lean:88
BanditRLProof.CurvatureNoiseGap.IsSimplexTangent definition Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:29
BanditRLProof.CurvatureNoiseGap.tangentPairing definition Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:34
BanditRLProof.CurvatureNoiseGap.tangentPairing_add_const_of_isSimplexTangent theorem Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:39
BanditRLProof.CurvatureNoiseGap.weightedShiftEnergy definition Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:50
BanditRLProof.CurvatureNoiseGap.weightedCenter definition Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:55
BanditRLProof.CurvatureNoiseGap.sum_weight_mul_sub_weightedCenter_eq_zero theorem Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:60
BanditRLProof.CurvatureNoiseGap.weightedShiftEnergy_decomposition_of_centered theorem Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:73
BanditRLProof.CurvatureNoiseGap.weightedShiftEnergy_decomposition theorem Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:103
BanditRLProof.CurvatureNoiseGap.weightedShiftEnergy_center_le theorem Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:117
BanditRLProof.CurvatureNoiseGap.weightedShiftEnergy_eq_center_iff theorem Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:129
BanditRLProof.CurvatureNoiseGap.weightedShiftEnergy_add_decomposition theorem Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:153
BanditRLProof.CurvatureNoiseGap.weightedShiftEnergy_add_le_two theorem Foundations BanditRLProof.CurvatureNoiseGapGeometry Compiled BanditRLProof/CurvatureNoiseGapGeometry.lean:182
BanditRLProof.DelayedFeedback.observedBefore definition Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:12
BanditRLProof.DelayedFeedback.outstandingAt definition Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:18
BanditRLProof.DelayedFeedback.observedBefore_disjoint_outstandingAt theorem Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:22
BanditRLProof.DelayedFeedback.observedBefore_union_outstandingAt theorem Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:30
BanditRLProof.DelayedFeedback.card_observedBefore_add_card_outstandingAt theorem Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:46
BanditRLProof.DelayedFeedback.outstandingCount definition Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:58
BanditRLProof.DelayedFeedback.maxOutstandingBeforeThrough definition Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:62
BanditRLProof.DelayedFeedback.outstandingCount_le_round theorem Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:67
BanditRLProof.DelayedFeedback.outstandingCount_le_maxOutstandingBeforeThrough theorem Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:75
BanditRLProof.DelayedFeedback.oneBasedDelayShift definition Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:86
BanditRLProof.DelayedFeedback.paperMissingAtEnd definition Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:92
BanditRLProof.DelayedFeedback.paperMissingAtEnd_eq_outstandingAt_oneBasedDelayShift theorem Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:99
BanditRLProof.DelayedFeedback.paperMissingCount definition Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:113
BanditRLProof.DelayedFeedback.paperMissingCount_eq_outstandingCount_oneBasedDelayShift theorem Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:117
BanditRLProof.DelayedFeedback.paperMissingCount_le_round theorem Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:124
BanditRLProof.DelayedFeedback.paperSigmaMaxThrough definition Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:131
BanditRLProof.DelayedFeedback.paperMissingCount_le_paperSigmaMaxThrough theorem Frontier BanditRLProof.DelayedFeedback.Accounting Compiled BanditRLProof/DelayedFeedback/Accounting.lean:136
BanditRLProof.DelayedFeedback.DelayedSAPOAllocation structure Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:13
BanditRLProof.DelayedFeedback.DelayedSAPOAllocation.probability definition Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:26
BanditRLProof.DelayedFeedback.DelayedSAPOAllocation.probability_nonnegative theorem Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:30
BanditRLProof.DelayedFeedback.DelayedSAPOAllocation.sum_probability_eq_one theorem Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:37
BanditRLProof.DelayedFeedback.DelayedSAPOAllocation.finiteActionDistribution theorem Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:45
BanditRLProof.DelayedFeedback.DelayedSAPOAllocation.actionMeasure definition Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:57
BanditRLProof.DelayedFeedback.DelayedSAPOAllocation.actionMeasure_isProbabilityMeasure theorem Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:61
BanditRLProof.DelayedFeedback.causalDelayedSAPOActionMeasureRule definition Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:72
BanditRLProof.DelayedFeedback.causalDelayedSAPOActionMeasureRule_isProbabilityMeasure theorem Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:79
BanditRLProof.DelayedFeedback.causalDelayedSAPOActionMeasureRule_eq_of_observation_equivalent theorem Frontier BanditRLProof.DelayedFeedback.ActionLaw Compiled BanditRLProof/DelayedFeedback/ActionLaw.lean:89
BanditRLProof.DelayedFeedback.inactiveArms definition Frontier BanditRLProof.DelayedFeedback.ActiveAllocation Compiled BanditRLProof/DelayedFeedback/ActiveAllocation.lean:11
BanditRLProof.DelayedFeedback.activeEqualShare definition Frontier BanditRLProof.DelayedFeedback.ActiveAllocation Compiled BanditRLProof/DelayedFeedback/ActiveAllocation.lean:15
BanditRLProof.DelayedFeedback.delayedSAPOProbability definition Frontier BanditRLProof.DelayedFeedback.ActiveAllocation Compiled BanditRLProof/DelayedFeedback/ActiveAllocation.lean:22
BanditRLProof.DelayedFeedback.delayedSAPOProbability_of_active theorem Frontier BanditRLProof.DelayedFeedback.ActiveAllocation Compiled BanditRLProof/DelayedFeedback/ActiveAllocation.lean:29
BanditRLProof.DelayedFeedback.delayedSAPOProbability_of_inactive theorem Frontier BanditRLProof.DelayedFeedback.ActiveAllocation Compiled BanditRLProof/DelayedFeedback/ActiveAllocation.lean:37
BanditRLProof.DelayedFeedback.activeEqualShare_nonneg theorem Frontier BanditRLProof.DelayedFeedback.ActiveAllocation Compiled BanditRLProof/DelayedFeedback/ActiveAllocation.lean:46
BanditRLProof.DelayedFeedback.delayedSAPOProbability_nonneg theorem Frontier BanditRLProof.DelayedFeedback.ActiveAllocation Compiled BanditRLProof/DelayedFeedback/ActiveAllocation.lean:54
BanditRLProof.DelayedFeedback.sum_delayedSAPOProbability_eq_one theorem Frontier BanditRLProof.DelayedFeedback.ActiveAllocation Compiled BanditRLProof/DelayedFeedback/ActiveAllocation.lean:68
BanditRLProof.DelayedFeedback.ActionTimeView structure Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:16
BanditRLProof.DelayedFeedback.ActionTimeView.ext theorem Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:21
BanditRLProof.DelayedFeedback.actionTimeViewAt definition Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:36
BanditRLProof.DelayedFeedback.CausalDecisionRule abbreviation Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:47
BanditRLProof.DelayedFeedback.actionTimeViewAt_pastAction_of_lt theorem Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:52
BanditRLProof.DelayedFeedback.actionTimeViewAt_pastAction_of_not_lt theorem Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:60
BanditRLProof.DelayedFeedback.actionTimeViewAt_observedLoss_of_mem theorem Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:68
BanditRLProof.DelayedFeedback.actionTimeViewAt_observedLoss_of_not_mem theorem Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:76
BanditRLProof.DelayedFeedback.actionTimeViewAt_outstanding_loss_hidden theorem Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:84
BanditRLProof.DelayedFeedback.actionTimeViewAt_eq_of_observation_equivalent theorem Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:96
BanditRLProof.DelayedFeedback.causalDecision_eq_of_observation_equivalent theorem Frontier BanditRLProof.DelayedFeedback.CausalView Compiled BanditRLProof/DelayedFeedback/CausalView.lean:122
BanditRLProof.DelayedFeedback.DelayedSAPOEliminationSnapshot structure Frontier BanditRLProof.DelayedFeedback.Elimination Compiled BanditRLProof/DelayedFeedback/Elimination.lean:12
BanditRLProof.DelayedFeedback.DelayedSAPOEliminationSnapshot.eliminated definition Frontier BanditRLProof.DelayedFeedback.Elimination Compiled BanditRLProof/DelayedFeedback/Elimination.lean:21
BanditRLProof.DelayedFeedback.DelayedSAPOEliminationSnapshot.remainingActive definition Frontier BanditRLProof.DelayedFeedback.Elimination Compiled BanditRLProof/DelayedFeedback/Elimination.lean:29
BanditRLProof.DelayedFeedback.DelayedSAPOEliminationSnapshot.mem_eliminated_iff theorem Frontier BanditRLProof.DelayedFeedback.Elimination Compiled BanditRLProof/DelayedFeedback/Elimination.lean:35
BanditRLProof.DelayedFeedback.DelayedSAPOEliminationSnapshot.mem_remainingActive_iff theorem Frontier BanditRLProof.DelayedFeedback.Elimination Compiled BanditRLProof/DelayedFeedback/Elimination.lean:45
BanditRLProof.DelayedFeedback.DelayedSAPOEliminationSnapshot.OptimalArmSurvivalCertificate structure Frontier BanditRLProof.DelayedFeedback.Elimination Compiled BanditRLProof/DelayedFeedback/Elimination.lean:61
BanditRLProof.DelayedFeedback.DelayedSAPOEliminationSnapshot.optimal_mem_remainingActive_of_certificate theorem Frontier BanditRLProof.DelayedFeedback.Elimination Compiled BanditRLProof/DelayedFeedback/Elimination.lean:74
BanditRLProof.DelayedFeedback.DelayedSAPOEliminationSnapshot.remainingActive_nonempty_of_certificate theorem Frontier BanditRLProof.DelayedFeedback.Elimination Compiled BanditRLProof/DelayedFeedback/Elimination.lean:92
BanditRLProof.DelayedFeedback.DelayedSAPOEliminationSnapshot.sum_delayedSAPOProbability_after_elimination_eq_one theorem Frontier BanditRLProof.DelayedFeedback.Elimination Compiled BanditRLProof/DelayedFeedback/Elimination.lean:103
BanditRLProof.DelayedFeedback.SameAlgorithmMultiRegimeContract structure Frontier BanditRLProof.DelayedFeedback.MultiRegimeContract Compiled BanditRLProof/DelayedFeedback/MultiRegimeContract.lean:15
BanditRLProof.DelayedFeedback.SameAlgorithmMultiRegimeContract.stochasticClaim definition Frontier BanditRLProof.DelayedFeedback.MultiRegimeContract Compiled BanditRLProof/DelayedFeedback/MultiRegimeContract.lean:39
BanditRLProof.DelayedFeedback.SameAlgorithmMultiRegimeContract.adversarialClaim definition Frontier BanditRLProof.DelayedFeedback.MultiRegimeContract Compiled BanditRLProof/DelayedFeedback/MultiRegimeContract.lean:56
BanditRLProof.DelayedFeedback.SameAlgorithmMultiRegimeContract.stochasticClaim_iff_shared_fields theorem Frontier BanditRLProof.DelayedFeedback.MultiRegimeContract Compiled BanditRLProof/DelayedFeedback/MultiRegimeContract.lean:71
BanditRLProof.DelayedFeedback.SameAlgorithmMultiRegimeContract.adversarialClaim_iff_shared_fields theorem Frontier BanditRLProof.DelayedFeedback.MultiRegimeContract Compiled BanditRLProof/DelayedFeedback/MultiRegimeContract.lean:88
BanditRLProof.DelayedFeedback.newlyObservedBefore definition Frontier BanditRLProof.DelayedFeedback.Processing Compiled BanditRLProof/DelayedFeedback/Processing.lean:10
BanditRLProof.DelayedFeedback.observedBefore_mono theorem Frontier BanditRLProof.DelayedFeedback.Processing Compiled BanditRLProof/DelayedFeedback/Processing.lean:16
BanditRLProof.DelayedFeedback.processed_disjoint_newlyObservedBefore theorem Frontier BanditRLProof.DelayedFeedback.Processing Compiled BanditRLProof/DelayedFeedback/Processing.lean:25
BanditRLProof.DelayedFeedback.processed_union_newlyObservedBefore theorem Frontier BanditRLProof.DelayedFeedback.Processing Compiled BanditRLProof/DelayedFeedback/Processing.lean:34
BanditRLProof.DelayedFeedback.processAllNew definition Frontier BanditRLProof.DelayedFeedback.Processing Compiled BanditRLProof/DelayedFeedback/Processing.lean:52
BanditRLProof.DelayedFeedback.processAllNew_eq_observedBefore theorem Frontier BanditRLProof.DelayedFeedback.Processing Compiled BanditRLProof/DelayedFeedback/Processing.lean:56
BanditRLProof.DelayedFeedback.previousObservedBefore_subset_current theorem Frontier BanditRLProof.DelayedFeedback.Processing Compiled BanditRLProof/DelayedFeedback/Processing.lean:63
BanditRLProof.DelayedFeedback.processAllNew_from_previous_eq_current theorem Frontier BanditRLProof.DelayedFeedback.Processing Compiled BanditRLProof/DelayedFeedback/Processing.lean:70
BanditRLProof.DelayedFeedback.outstandingAt_disjoint_newlyObservedBefore theorem Frontier BanditRLProof.DelayedFeedback.Processing Compiled BanditRLProof/DelayedFeedback/Processing.lean:79
BanditRLProof.DelayedFeedback.sourceEmpiricalWidthScale definition Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:12
BanditRLProof.DelayedFeedback.sourceEmpiricalWidthScale_antitone theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:18
BanditRLProof.DelayedFeedback.one_le_ten_mul_sourceEmpiricalWidthScale_of_count_le_96_mul_scale theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:35
BanditRLProof.DelayedFeedback.one_le_ten_mul_sourceEmpiricalWidthScale_two_log_of_small_count theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:58
BanditRLProof.DelayedFeedback.sourceEmpiricalWidthScale_one_one theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:70
BanditRLProof.DelayedFeedback.sourceEmpiricalWidthScale_one_four theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:77
BanditRLProof.DelayedFeedback.not_sourceEmpiricalWidthScale_one_le_four theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:85
BanditRLProof.DelayedFeedback.not_sourceEmpiricalWidthScale_horizon_four_one_le_four theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:94
BanditRLProof.DelayedFeedback.eight_mul_empiricalWidth_lt_gap_of_mem_eliminated theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:133
BanditRLProof.DelayedFeedback.gap_le_sixteen_mul_empiricalWidth_of_mem_remainingActive theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:158
BanditRLProof.DelayedFeedback.gap_le_sixteen_mul_empiricalWidth_of_mem_remainingActive_of_large_or_small_count theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:191
BanditRLProof.DelayedFeedback.gap_le_twenty_mul_gap_at_earlier_elimination_snapshot theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:229
BanditRLProof.DelayedFeedback.gap_le_twenty_mul_gap_at_earlier_elimination_snapshot_of_large_or_small_count theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:260
BanditRLProof.DelayedFeedback.DelayedSAPOD10D12GapOrderingContract structure Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:295
BanditRLProof.DelayedFeedback.DelayedSAPOD10D12GapOrderingContract.surrogateGap definition Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:312
BanditRLProof.DelayedFeedback.DelayedSAPOD10D12GapOrderingContract.surrogateGap_le_gap theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:318
BanditRLProof.DelayedFeedback.DelayedSAPOD10D12GapOrderingContract.gap_le_two_mul_surrogateGap theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:326
BanditRLProof.DelayedFeedback.DelayedSAPOD10D12GapOrderingContract.d12_gap_ordering_chain theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:337
BanditRLProof.DelayedFeedback.DelayedSAPOD10D12GapOrderingContract.gap_le_twenty_mul_gap_of_eliminationPrefixIndex_le theorem Frontier BanditRLProof.DelayedFeedback.StochasticGapOrderingAudit Compiled BanditRLProof/DelayedFeedback/StochasticGapOrderingAudit.lean:367
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot structure Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:13
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.sourceUcbStar definition Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:22
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.EliminationGoodEvent structure Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:31
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.optimalMean_le_ucbStar_of_eliminationGoodEvent theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:43
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.optimalArmSurvivalCertificate_of_eliminationGoodEvent theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:60
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.optimal_mem_remainingActive_of_eliminationGoodEvent theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:80
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.eliminationGoodEventSet definition Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:95
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.optimalSurvivalEventSet definition Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:101
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.eliminationGoodEventSet_subset_optimalSurvivalEventSet theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:108
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.measure_optimalSurvivalEventSet_compl_le theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:122
BanditRLProof.DelayedFeedback.DelayedSAPOSourceConfidenceSnapshot.measure_optimalSurvivalEventSet_compl_le_of_goodEvent theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEvent Compiled BanditRLProof/DelayedFeedback/StochasticGoodEvent.lean:141
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventComponent inductive type Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:13
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily structure Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:25
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.componentFailure definition Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:36
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.failureSet definition Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:47
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.sourceGoodEventSet definition Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:53
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.sourceGoodEventSet_compl theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:59
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.measure_sourceGoodEventSet_compl_le_sum theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:65
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.quadraticFailureBudget definition Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:77
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.linearFailureBudget definition Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:81
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.quadraticFailureBudget_le_linearFailureBudget theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:86
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.measure_sourceGoodEventSet_compl_le_nine_div theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:107
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.measure_eliminationGoodEventSet_compl_le_nine_div theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:175
BanditRLProof.DelayedFeedback.DelayedSAPOGoodEventFailureFamily.measure_optimalSurvivalEventSet_compl_le_nine_div theorem Frontier BanditRLProof.DelayedFeedback.StochasticGoodEventAssembly Compiled BanditRLProof/DelayedFeedback/StochasticGoodEventAssembly.lean:209
BanditRLProof.Exp3.MeasurableFiniteActionDistribution structure EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:22
BanditRLProof.Exp3.finiteActionKernel definition EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:31
BanditRLProof.Exp3.finiteActionKernel_apply theorem EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:48
BanditRLProof.Exp3.actionProcessMeasure definition EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:72
BanditRLProof.Exp3.actionProcessHistory definition EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:105
BanditRLProof.Exp3.actionProcessAction definition EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:109
BanditRLProof.Exp3.actionProcessHistory_measurable theorem EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:112
BanditRLProof.Exp3.actionProcessAction_measurable theorem EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:118
BanditRLProof.Exp3.actionProcess_history_map_eq theorem EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:125
BanditRLProof.Exp3.actionProcess_condDistrib_action_ae_eq_finiteActionKernel theorem EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:138
BanditRLProof.Exp3.finiteActionKernel_ae_eq_finiteActionMeasure theorem EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:160
BanditRLProof.Exp3.actionProcess_integral_importanceWeightedLoss_eq_integral_loss theorem EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:173
BanditRLProof.Exp3.actionProcess_integral_mixedImportanceWeightedLoss_eq_integral_mixedLoss theorem EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:208
BanditRLProof.Exp3.actionProcess_integral_mixedSquaredImportanceWeightedLoss_eq_integral_sum_loss_sq theorem EXP3 BanditRLProof.Exp3ActionProcess Compiled BanditRLProof/Exp3ActionProcess.lean:242
BanditRLProof.Exp3.predictableLossAt_nonneg theorem EXP3 BanditRLProof.Exp3BernsteinAllHorizon Compiled BanditRLProof/Exp3BernsteinAllHorizon.lean:22
BanditRLProof.Exp3.sampledPredictableTrajectoryMeasure_realizedLoss_le_one_ae theorem EXP3 BanditRLProof.Exp3BernsteinAllHorizon Compiled BanditRLProof/Exp3BernsteinAllHorizon.lean:35
BanditRLProof.Exp3.sampledPredictableTrajectoryMeasure_finiteHorizon_realizedLoss_le_one_ae theorem EXP3 BanditRLProof.Exp3BernsteinAllHorizon Compiled BanditRLProof/Exp3BernsteinAllHorizon.lean:59
BanditRLProof.Exp3.sampledPredictable_realizedRegret_le_horizon_ae theorem EXP3 BanditRLProof.Exp3BernsteinAllHorizon Compiled BanditRLProof/Exp3BernsteinAllHorizon.lean:85
BanditRLProof.Exp3.sampledPredictable_trivialRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3BernsteinAllHorizon Compiled BanditRLProof/Exp3BernsteinAllHorizon.lean:130
BanditRLProof.Exp3.bernsteinLargeHorizonCondition definition EXP3 BanditRLProof.Exp3BernsteinAllHorizon Compiled BanditRLProof/Exp3BernsteinAllHorizon.lean:172
BanditRLProof.Exp3.bernsteinAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3BernsteinAllHorizon Compiled BanditRLProof/Exp3BernsteinAllHorizon.lean:180
BanditRLProof.Exp3.sampledPredictable_allHorizonBernsteinRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3BernsteinAllHorizon Compiled BanditRLProof/Exp3BernsteinAllHorizon.lean:191
BanditRLProof.Exp3.bernsteinArmEntropyExplorationScale definition EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:19
BanditRLProof.Exp3.bernsteinConfidenceExplorationScale definition EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:24
BanditRLProof.Exp3.bernsteinRealizedExplorationScale definition EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:29
BanditRLProof.Exp3.bernsteinRawExplorationRate definition EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:37
BanditRLProof.Exp3.bernsteinClippedExplorationRate definition EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:45
BanditRLProof.Exp3.rpow_inv_three_le_half_of_eight_mul_le theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:51
BanditRLProof.Exp3.sqrt_div_le_half_of_four_mul_le theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:67
BanditRLProof.Exp3.numerator_le_cube_mul_of_rpow_inv_three_le theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:80
BanditRLProof.Exp3.numerator_le_sq_mul_of_sqrt_div_le theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:99
BanditRLProof.Exp3.bernsteinClippedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:111
BanditRLProof.Exp3.bernsteinClippedExplorationRate_eq_raw theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:116
BanditRLProof.Exp3.bernsteinRawExplorationRate_pos theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:125
BanditRLProof.Exp3.bernsteinClippedExplorationRate_pos theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:137
BanditRLProof.Exp3.bernsteinRawExplorationRate_le_half_of_horizon_contracts theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:146
BanditRLProof.Exp3.bernsteinClippedExplorationRate_contracts theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:181
BanditRLProof.Exp3.sampledPredictable_explicitBernsteinRealizedHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3BernsteinExplicitTuning Compiled BanditRLProof/Exp3BernsteinExplicitTuning.lean:250
BanditRLProof.Exp3.sampledPredictableBernsteinHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3BernsteinHighProbabilityRegret Compiled BanditRLProof/Exp3BernsteinHighProbabilityRegret.lean:21
BanditRLProof.Exp3.sampledPredictable_bernsteinHighProbabilityRegret_tail_delta theorem EXP3 BanditRLProof.Exp3BernsteinHighProbabilityRegret Compiled BanditRLProof/Exp3BernsteinHighProbabilityRegret.lean:35
BanditRLProof.Exp3.sampledPredictable_bernsteinHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3BernsteinHighProbabilityRegret Compiled BanditRLProof/Exp3BernsteinHighProbabilityRegret.lean:183
BanditRLProof.Exp3.sampledPredictableBernsteinRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3BernsteinRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3BernsteinRealizedHighProbabilityRegret.lean:25
BanditRLProof.Exp3.sampledPredictable_bernsteinRealizedHighProbabilityRegret_tail_delta theorem EXP3 BanditRLProof.Exp3BernsteinRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3BernsteinRealizedHighProbabilityRegret.lean:35
BanditRLProof.Exp3.sampledPredictable_bernsteinRealizedHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3BernsteinRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3BernsteinRealizedHighProbabilityRegret.lean:148
BanditRLProof.Exp3.bernsteinHighProbabilityLearningRate definition EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:21
BanditRLProof.Exp3.bernsteinConfidenceRadius_le_three_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:27
BanditRLProof.Exp3.realizedDeviationRadius_le_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:69
BanditRLProof.Exp3.bernsteinHighProbabilityLearningRate_pos theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:83
BanditRLProof.Exp3.bernsteinHighProbabilityLearningRate_sq_mul theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:92
BanditRLProof.Exp3.bernsteinHighProbabilityLearningRate_le_sq_div theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:105
BanditRLProof.Exp3.bernsteinEntropyBudget_le_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:126
BanditRLProof.Exp3.bernsteinUnscaledSquareBudget_le_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:157
BanditRLProof.Exp3.bernsteinHedgeBudget_le_three_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:182
BanditRLProof.Exp3.log_one_div_third_eq_log_three_div theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:218
BanditRLProof.Exp3.sampledPredictableBernsteinRealizedHighProbabilityRegretBudget_le_eleven_mul theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:225
BanditRLProof.Exp3.sampledPredictable_tunedBernsteinRealizedHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3BernsteinTuning Compiled BanditRLProof/Exp3BernsteinTuning.lean:316
BanditRLProof.Exp3.sampledPredictableBestArmCumulativeLoss definition EXP3 BanditRLProof.Exp3BestArm Compiled BanditRLProof/Exp3BestArm.lean:17
BanditRLProof.Exp3.threshold_le_sampledPredictableRealizedLoss_sub_bestArmCumulativeLoss_iff theorem EXP3 BanditRLProof.Exp3BestArm Compiled BanditRLProof/Exp3BestArm.lean:29
BanditRLProof.Concentration.exp_le_one_add_self_add_sq_of_abs_le_one theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:20
BanditRLProof.Concentration.exists_tilt_fixedMGF_exponent_le_neg theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:27
BanditRLProof.Exp3.sum_prob_mul_sq_comparatorEstimatorDeviation_eq theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:115
BanditRLProof.Exp3.sum_prob_mul_sq_comparatorEstimatorDeviation_le_inv_floor theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:151
BanditRLProof.Exp3.finiteActionComparatorEstimator_hasMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:176
BanditRLProof.Exp3.comparatorEstimator_hasCondMGFUpperBoundAt_of_condDistrib_ae_eq_finiteActionKernel theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:283
BanditRLProof.Exp3.sampledPredictableComparatorEstimatorDeviation_zero_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:421
BanditRLProof.Exp3.sampledPredictableComparatorEstimatorDeviation_succ_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:478
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviation_zero_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:535
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviation_succ_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:600
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviation_sum_tail_fixedTilt theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:674
BanditRLProof.Exp3.sampledComparatorEstimatorBernsteinConfidenceRadius definition EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:752
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviation_sum_tail_bernstein_delta theorem EXP3 BanditRLProof.Exp3ComparatorBernstein Compiled BanditRLProof/Exp3ComparatorBernstein.lean:762
BanditRLProof.Exp3.comparatorEstimator_hasCondSubgaussianMGF_of_condDistrib_ae_eq_finiteActionKernel theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:9
BanditRLProof.Exp3.sampledTrajectoryPredictableComparatorEstimatorDeviationAt definition EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:159
BanditRLProof.Exp3.sampledTrajectoryObservedComparatorEstimatorDeviationAt definition EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:170
BanditRLProof.Exp3.sampledPredictableComparatorEstimatorDeviation_zero_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:179
BanditRLProof.Exp3.sampledPredictableComparatorEstimatorDeviation_succ_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:234
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviation_zero_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:289
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviation_succ_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:354
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviationProcess definition EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:426
BanditRLProof.Exp3.sampledComparatorEstimatorVarianceProxy definition EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:437
BanditRLProof.Exp3.sampledComparatorEstimatorDeviationProxy definition EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:442
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviationProcess_stronglyAdapted theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:447
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviationProcess_sum_range_succ theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:600
BanditRLProof.Exp3.sampledComparatorEstimatorDeviationProxy_sum_range_succ theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:638
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviation_sum_tail_ennreal theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:655
BanditRLProof.Exp3.sampledComparatorEstimatorConfidenceRadius definition EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:725
BanditRLProof.Exp3.sampledComparatorEstimatorVarianceProxy_pos theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:733
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviation_sum_tail_exp_neg_budget theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:750
BanditRLProof.Exp3.sampledObservedComparatorEstimatorDeviation_sum_tail_delta theorem EXP3 BanditRLProof.Exp3ComparatorConfidence Compiled BanditRLProof/Exp3ComparatorConfidence.lean:800
BanditRLProof.Exp3.FiniteActionDistribution structure EXP3 BanditRLProof.Exp3ConditionalMoments Compiled BanditRLProof/Exp3ConditionalMoments.lean:22
BanditRLProof.Exp3.finiteActionMeasure definition EXP3 BanditRLProof.Exp3ConditionalMoments Compiled BanditRLProof/Exp3ConditionalMoments.lean:28
BanditRLProof.Exp3.finiteActionMeasure_isProbabilityMeasure theorem EXP3 BanditRLProof.Exp3ConditionalMoments Compiled BanditRLProof/Exp3ConditionalMoments.lean:33
BanditRLProof.Exp3.integral_finiteActionMeasure_eq_sum theorem EXP3 BanditRLProof.Exp3ConditionalMoments Compiled BanditRLProof/Exp3ConditionalMoments.lean:42
BanditRLProof.Exp3.integral_historyAction_eq_integral_sum_of_condDistrib_ae_eq_finiteActionMeasure theorem EXP3 BanditRLProof.Exp3ConditionalMoments Compiled BanditRLProof/Exp3ConditionalMoments.lean:60
BanditRLProof.Exp3.integral_importanceWeightedLoss_eq_integral_loss_of_condDistrib theorem EXP3 BanditRLProof.Exp3ConditionalMoments Compiled BanditRLProof/Exp3ConditionalMoments.lean:100
BanditRLProof.Exp3.integral_mixedImportanceWeightedLoss_eq_integral_mixedLoss_of_condDistrib theorem EXP3 BanditRLProof.Exp3ConditionalMoments Compiled BanditRLProof/Exp3ConditionalMoments.lean:138
BanditRLProof.Exp3.integral_weightedImportanceWeightedLoss_eq_integral_weightedLoss_of_condDistrib theorem EXP3 BanditRLProof.Exp3ConditionalMoments Compiled BanditRLProof/Exp3ConditionalMoments.lean:177
BanditRLProof.Exp3.integral_mixedSquaredImportanceWeightedLoss_eq_integral_sum_loss_sq_of_condDistrib theorem EXP3 BanditRLProof.Exp3ConditionalMoments Compiled BanditRLProof/Exp3ConditionalMoments.lean:216
BanditRLProof.Exp3.eventually_const_le_natCast theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:20
BanditRLProof.Exp3.eventually_const_le_natCast_pow_three theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:26
BanditRLProof.Exp3.eventually_doubleVarianceProbabilisticSparseLossLargeHorizonCondition theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:45
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossBestArmAllHorizonRegretThreshold_eq_explicit_of_largeHorizon theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:61
BanditRLProof.Exp3.sampledPredictable_explicitDoubleVarianceProbabilisticSparseLossBestArmRealizedRegret_tail_off_sparsityFailure_of_largeHorizon theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:84
BanditRLProof.Exp3.sampledPredictable_explicitDoubleVarianceProbabilisticSparseLossBestArmRealizedRegret_tail_of_largeHorizon theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:143
BanditRLProof.Exp3.sampledPredictable_explicitDoubleVarianceProbabilisticSparseLossBestArmRealizedRegret_tail_of_sparsityFailure_le_of_largeHorizon theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:203
BanditRLProof.Exp3.eventually_sampledPredictable_explicitDoubleVarianceProbabilisticSparseLossBestArmRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:266
BanditRLProof.Exp3.eventually_sampledPredictable_explicitDoubleVarianceProbabilisticSparseLossBestArmRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:326
BanditRLProof.Exp3.eventually_sampledPredictable_explicitDoubleVarianceProbabilisticSparseLossBestArmRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3DoubleVarianceSparseBestArmEventualRefinedRegret Compiled BanditRLProof/Exp3DoubleVarianceSparseBestArmEventualRefinedRegret.lean:387
BanditRLProof.Exp3.expectedRegretBudget_le_four_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:22
BanditRLProof.Exp3.tunedExplorationRate definition EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:54
BanditRLProof.Exp3.tunedLearningRate definition EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:58
BanditRLProof.Exp3.tunedExplorationRate_pos theorem EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:61
BanditRLProof.Exp3.tunedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:67
BanditRLProof.Exp3.tunedLearningRate_pos theorem EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:77
BanditRLProof.Exp3.tunedExplorationRate_sq_mul_eq theorem EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:82
BanditRLProof.Exp3.tunedExplorationRate_mul_eq_sqrt_mul theorem EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:90
BanditRLProof.Exp3.sampledPredictable_expectedRegret_le_four_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:110
BanditRLProof.Exp3.tunedPredictableTrajectoryKernel definition EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:153
BanditRLProof.Exp3.sampledPredictable_expectedRegret_le_four_mul_sqrt theorem EXP3 BanditRLProof.Exp3ExpectedRegret Compiled BanditRLProof/Exp3ExpectedRegret.lean:181
BanditRLProof.Exp3.distribution_le_sampledTrajectoryProbabilityAt_div_one_sub_gamma theorem EXP3 BanditRLProof.Exp3ExplorationBias Compiled BanditRLProof/Exp3ExplorationBias.lean:24
BanditRLProof.Exp3.mixedSquaredLoss_sampledTrajectoryObservedLoss_le_inv_one_sub_gamma theorem EXP3 BanditRLProof.Exp3ExplorationBias Compiled BanditRLProof/Exp3ExplorationBias.lean:50
BanditRLProof.Exp3.sampledTrajectoryPredictableMixedLoss_le_pure_add_gamma theorem EXP3 BanditRLProof.Exp3ExplorationBias Compiled BanditRLProof/Exp3ExplorationBias.lean:90
BanditRLProof.Exp3.sampledTrajectory_finiteHorizon_explorationBias_secondMoment theorem EXP3 BanditRLProof.Exp3ExplorationBias Compiled BanditRLProof/Exp3ExplorationBias.lean:180
BanditRLProof.Exp3.cumulativeLoss definition EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:30
BanditRLProof.Exp3.weight definition EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:35
BanditRLProof.Exp3.totalWeight definition EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:40
BanditRLProof.Exp3.distribution definition EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:46
BanditRLProof.Exp3.mixedLoss definition EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:52
BanditRLProof.Exp3.mixedSquaredLoss definition EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:58
BanditRLProof.Exp3.cumulativeLoss_succ theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:63
BanditRLProof.Exp3.weight_pos theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:68
BanditRLProof.Exp3.weight_succ theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:73
BanditRLProof.Exp3.totalWeight_pos theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:83
BanditRLProof.Exp3.distribution_nonneg theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:92
BanditRLProof.Exp3.distribution_pos theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:99
BanditRLProof.Exp3.sum_distribution theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:106
BanditRLProof.Exp3.totalWeight_zero theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:117
BanditRLProof.Exp3.exp_neg_le_one_sub_add_sq theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:123
BanditRLProof.Exp3.exp_neg_mul_le_one_sub_add_sq_of_nonneg theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:140
BanditRLProof.Exp3.exp_neg_mul_le_one_sub_add_sq theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:147
BanditRLProof.Exp3.totalWeight_succ_div_eq_sum_distribution_mul_exp theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:153
BanditRLProof.Exp3.totalWeight_succ_div_le_of_nonneg theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:169
BanditRLProof.Exp3.totalWeight_succ_div_le theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:218
BanditRLProof.Exp3.log_totalWeight_succ_sub_le_of_nonneg theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:231
BanditRLProof.Exp3.log_totalWeight_succ_sub_le theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:249
BanditRLProof.Exp3.mixedSquaredLoss_le_one theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:262
BanditRLProof.Exp3.hedge_regret_le_log_card_div_add_eta_mul_mixedSquaredLoss_of_nonneg theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:283
BanditRLProof.Exp3.hedge_regret_le_log_card_div_add_eta_mul_mixedSquaredLoss theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:359
BanditRLProof.Exp3.hedge_regret_le_log_card_div_add_eta_mul_horizon theorem EXP3 BanditRLProof.Exp3HedgeRegret Compiled BanditRLProof/Exp3HedgeRegret.lean:382
BanditRLProof.Exp3.observedMixedSquaredImportanceWeightedLossAt_le_inv_explorationFloor theorem EXP3 BanditRLProof.Exp3HighProbabilityRegret Compiled BanditRLProof/Exp3HighProbabilityRegret.lean:24
BanditRLProof.Exp3.sampledPredictableTrajectoryMeasure_reward_mem_unitInterval_ae theorem EXP3 BanditRLProof.Exp3HighProbabilityRegret Compiled BanditRLProof/Exp3HighProbabilityRegret.lean:70
BanditRLProof.Exp3.sampledPredictableTrajectoryMeasure_observedMixedSquared_sum_le_ae theorem EXP3 BanditRLProof.Exp3HighProbabilityRegret Compiled BanditRLProof/Exp3HighProbabilityRegret.lean:113
BanditRLProof.Exp3.sampledPredictableHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3HighProbabilityRegret Compiled BanditRLProof/Exp3HighProbabilityRegret.lean:158
BanditRLProof.Exp3.sampledPredictable_highProbabilityRegret_tail_delta theorem EXP3 BanditRLProof.Exp3HighProbabilityRegret Compiled BanditRLProof/Exp3HighProbabilityRegret.lean:171
BanditRLProof.Exp3.sampledPredictable_highProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3HighProbabilityRegret Compiled BanditRLProof/Exp3HighProbabilityRegret.lean:319
BanditRLProof.Exp3.importanceWeightedLoss definition EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:25
BanditRLProof.Exp3.mixedImportanceWeightedLoss definition EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:31
BanditRLProof.Exp3.weightedImportanceWeightedLoss definition EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:38
BanditRLProof.Exp3.mixedSquaredImportanceWeightedLoss definition EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:45
BanditRLProof.Exp3.importanceWeightedLoss_nonneg theorem EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:50
BanditRLProof.Exp3.sum_prob_mul_importanceWeightedLoss_eq_loss theorem EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:60
BanditRLProof.Exp3.mixedImportanceWeightedLoss_eq_selectedLoss theorem EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:77
BanditRLProof.Exp3.sum_prob_mul_mixedImportanceWeightedLoss_eq_mixedLoss theorem EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:93
BanditRLProof.Exp3.sum_prob_mul_weightedImportanceWeightedLoss_eq_weightedLoss theorem EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:107
BanditRLProof.Exp3.mixedSquaredImportanceWeightedLoss_eq_selectedLoss_sq_div theorem EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:135
BanditRLProof.Exp3.sum_prob_mul_mixedSquaredImportanceWeightedLoss_eq_sum_loss_sq theorem EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:151
BanditRLProof.Exp3.sum_prob_mul_mixedSquaredImportanceWeightedLoss_le_card theorem EXP3 BanditRLProof.Exp3ImportanceWeighted Compiled BanditRLProof/Exp3ImportanceWeighted.lean:166
BanditRLProof.Exp3.sum_prob_mul_sq_mixedSquaredImportanceWeightedLoss_eq theorem EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:25
BanditRLProof.Exp3.sum_prob_mul_sq_mixedSquaredEstimatorDeviation_le_card_div_floor theorem EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:41
BanditRLProof.Exp3.finiteActionMixedSquaredEstimator_hasMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:111
BanditRLProof.Exp3.mixedSquaredEstimator_hasCondMGFUpperBoundAt_of_condDistrib_ae_eq_finiteActionKernel theorem EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:232
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_zero_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:372
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_succ_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:429
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_sum_tail_fixedTilt theorem EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:488
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_bernstein_fixedTilt theorem EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:582
BanditRLProof.Exp3.sampledMixedSquaredBernsteinVarianceCoefficient definition EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:628
BanditRLProof.Exp3.sampledMixedSquaredBernsteinConfidenceRadius definition EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:633
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_bernstein_delta theorem EXP3 BanditRLProof.Exp3MixedSquareBernstein Compiled BanditRLProof/Exp3MixedSquareBernstein.lean:645
BanditRLProof.Exp3.sampledPredictableBernsteinSquareHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareBernsteinHighProbabilityRegret.lean:21
BanditRLProof.Exp3.sampledPredictable_bernsteinSquareHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareBernsteinHighProbabilityRegret.lean:37
BanditRLProof.Exp3.sampledPredictable_bernsteinSquareHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareBernsteinHighProbabilityRegret.lean:199
BanditRLProof.Exp3.bernsteinSquareLargeHorizonCondition definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedAllHorizon Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedAllHorizon.lean:22
BanditRLProof.Exp3.bernsteinSquareAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedAllHorizon Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedAllHorizon.lean:33
BanditRLProof.Exp3.sampledPredictable_allHorizonBernsteinSquareRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedAllHorizon Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedAllHorizon.lean:49
BanditRLProof.Exp3.bernsteinSquareBestArmAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedBestArmAllHorizon.lean:21
BanditRLProof.Exp3.sampledPredictable_allHorizonBernsteinSquareBestArmRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedBestArmAllHorizon.lean:30
BanditRLProof.Exp3.sampledMixedSquaredBernsteinVarianceCoefficient_eq_card_sq_div_gamma theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:25
BanditRLProof.Exp3.log_mul_sampledMixedSquaredBernsteinConfidenceRadius_le_three_mul_sq_mul_horizon_sq theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:38
BanditRLProof.Exp3.bernsteinSquareBalancedSqrt_le_two_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:162
BanditRLProof.Exp3.bernsteinSquareRealizedExplicitThreshold definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:220
BanditRLProof.Exp3.bernsteinSquareRealizedTunedThreshold_le_explicitThreshold theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:229
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedBernsteinSquareRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:318
BanditRLProof.Exp3.bernsteinSquareClippedExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:393
BanditRLProof.Exp3.bernsteinSquareClippedExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:397
BanditRLProof.Exp3.bernsteinSquareClippedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:404
BanditRLProof.Exp3.bernsteinSquareClippedExplorationRate_contracts theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:412
BanditRLProof.Exp3.sampledPredictable_explicitBernsteinSquareRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedExplicitTuning.lean:438
BanditRLProof.Exp3.sampledPredictableBernsteinSquareRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedHighProbabilityRegret.lean:26
BanditRLProof.Exp3.sampledPredictable_bernsteinSquareRealizedHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedHighProbabilityRegret.lean:36
BanditRLProof.Exp3.sampledPredictable_bernsteinSquareRealizedHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedHighProbabilityRegret.lean:157
BanditRLProof.Exp3.bernsteinSquareHighProbabilityScale definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedTuning.lean:27
BanditRLProof.Exp3.bernsteinSquareHighProbabilityScale_pos theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedTuning.lean:33
BanditRLProof.Exp3.bernsteinSquareHighProbabilityLearningRate definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedTuning.lean:61
BanditRLProof.Exp3.bernsteinSquareHighProbabilityLearningRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedTuning.lean:68
BanditRLProof.Exp3.bernsteinSquareHighProbabilityLearningRate_sq_mul_scale theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedTuning.lean:81
BanditRLProof.Exp3.bernsteinSquareHighProbabilityHedgeBudget_le_three_mul_sqrt theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedTuning.lean:99
BanditRLProof.Exp3.bernsteinSquareRealizedTunedThreshold definition EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedTuning.lean:170
BanditRLProof.Exp3.sampledPredictableBernsteinSquareRealizedHighProbabilityRegretBudget_le_tunedThreshold theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedTuning.lean:185
BanditRLProof.Exp3.sampledPredictable_tunedBernsteinSquareRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3MixedSquareBernsteinRealizedTuning.lean:211
BanditRLProof.Exp3.mixedSquaredImportanceWeightedLoss_le_inv_floor theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:26
BanditRLProof.Exp3.mixedSquaredEstimator_hasCondSubgaussianMGF_of_condDistrib_ae_eq_finiteActionKernel theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:64
BanditRLProof.Exp3.sampledTrajectoryPredictableMixedSquaredDeviationAt definition EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:218
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_zero_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:229
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_succ_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:283
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviationProcess definition EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:340
BanditRLProof.Exp3.sampledMixedSquaredVarianceProxy definition EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:351
BanditRLProof.Exp3.sampledMixedSquaredDeviationProxy definition EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:356
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviationProcess_stronglyAdapted theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:362
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviationProcess_sum_range_succ theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:521
BanditRLProof.Exp3.sampledMixedSquaredDeviationProxy_sum_range_succ theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:541
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_sum_tail_ennreal theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:556
BanditRLProof.Exp3.sampledPredictableMixedSquaredSum definition EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:623
BanditRLProof.Exp3.sampledPredictableLossSquaredSum definition EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:634
BanditRLProof.Exp3.sampledPredictableLossSquaredAt_le_card theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:642
BanditRLProof.Exp3.sampledPredictableLossSquaredSum_le_card_mul theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:666
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_sum_eq theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:683
BanditRLProof.Exp3.sampledPredictableMixedSquared_sum_tail_ennreal theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:698
BanditRLProof.Exp3.sampledObservedMixedSquaredSum_eq_predictable_ae theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:744
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_exponential theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:775
BanditRLProof.Exp3.sampledMixedSquaredConfidenceRadius definition EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:816
BanditRLProof.Exp3.sampledMixedSquaredVarianceProxy_pos theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:824
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_exp_neg_budget theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:841
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_delta theorem EXP3 BanditRLProof.Exp3MixedSquareConfidence Compiled BanditRLProof/Exp3MixedSquareConfidence.lean:889
BanditRLProof.Exp3.sampledPredictableExponentialSquareBernsteinHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquareExponentialHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareExponentialHighProbabilityRegret.lean:24
BanditRLProof.Exp3.sampledPredictable_exponentialSquareBernsteinHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareExponentialHighProbabilityRegret.lean:39
BanditRLProof.Exp3.sampledPredictable_exponentialSquareBernsteinHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareExponentialHighProbabilityRegret.lean:201
BanditRLProof.Exp3.exponentialSquareBernsteinLargeHorizonCondition definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedAllHorizon Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedAllHorizon.lean:22
BanditRLProof.Exp3.exponentialSquareBernsteinAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedAllHorizon Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedAllHorizon.lean:33
BanditRLProof.Exp3.sampledPredictable_allHorizonExponentialSquareBernsteinRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedAllHorizon Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedAllHorizon.lean:50
BanditRLProof.Exp3.sampledMixedSquaredVarianceProxy_coe_eq_card_div_two_gamma_sq theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:22
BanditRLProof.Exp3.log_mul_sampledMixedSquaredConfidenceRadius_le_sq_mul_horizon_sq theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:39
BanditRLProof.Exp3.exponentialSquareBalancedSqrt_le_two_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:105
BanditRLProof.Exp3.exponentialSquareBernsteinRealizedExplicitThreshold definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:151
BanditRLProof.Exp3.exponentialSquareBernsteinRealizedTunedThreshold_le_explicitThreshold theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:158
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedExponentialSquareBernsteinRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:249
BanditRLProof.Exp3.exponentialSquareArmExplorationScale definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:329
BanditRLProof.Exp3.exponentialSquareMixedExplorationScale definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:335
BanditRLProof.Exp3.exponentialSquareBernsteinRawExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:342
BanditRLProof.Exp3.exponentialSquareBernsteinClippedExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:350
BanditRLProof.Exp3.rpow_inv_six_le_half_of_sixtyfour_mul_le theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:356
BanditRLProof.Exp3.numerator_le_pow_six_mul_of_rpow_inv_six_le theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:374
BanditRLProof.Exp3.exponentialSquareBernsteinClippedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:395
BanditRLProof.Exp3.exponentialSquareBernsteinClippedExplorationRate_eq_raw theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:400
BanditRLProof.Exp3.exponentialSquareBernsteinRawExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:407
BanditRLProof.Exp3.exponentialSquareBernsteinClippedExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:416
BanditRLProof.Exp3.exponentialSquareBernsteinRawExplorationRate_le_half_of_horizon_contracts theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:426
BanditRLProof.Exp3.exponentialSquareBernsteinClippedExplorationRate_contracts theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:473
BanditRLProof.Exp3.sampledPredictable_explicitExponentialSquareBernsteinRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedExplicitTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedExplicitTuning.lean:571
BanditRLProof.Exp3.sampledPredictableExponentialSquareBernsteinRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedHighProbabilityRegret.lean:25
BanditRLProof.Exp3.sampledPredictable_exponentialSquareBernsteinRealizedHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedHighProbabilityRegret.lean:35
BanditRLProof.Exp3.sampledPredictable_exponentialSquareBernsteinRealizedHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedHighProbabilityRegret.lean:157
BanditRLProof.Exp3.exponentialSquareHighProbabilityScale definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedTuning.lean:25
BanditRLProof.Exp3.exponentialSquareHighProbabilityScale_pos theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedTuning.lean:31
BanditRLProof.Exp3.exponentialSquareHighProbabilityLearningRate definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedTuning.lean:49
BanditRLProof.Exp3.exponentialSquareHighProbabilityLearningRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedTuning.lean:56
BanditRLProof.Exp3.exponentialSquareHighProbabilityLearningRate_sq_mul_scale theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedTuning.lean:68
BanditRLProof.Exp3.exponentialSquareHighProbabilityHedgeBudget_le_three_mul_sqrt theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedTuning.lean:85
BanditRLProof.Exp3.exponentialSquareBernsteinRealizedTunedThreshold definition EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedTuning.lean:156
BanditRLProof.Exp3.sampledPredictableExponentialSquareBernsteinRealizedHighProbabilityRegretBudget_le_tunedThreshold theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedTuning.lean:171
BanditRLProof.Exp3.sampledPredictable_tunedExponentialSquareBernsteinRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquareExponentialRealizedTuning Compiled BanditRLProof/Exp3MixedSquareExponentialRealizedTuning.lean:198
BanditRLProof.Exp3.mixedSquaredEstimatorCenteredSecondMoment definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:21
BanditRLProof.Exp3.measurable_mixedSquaredEstimatorCenteredSecondMoment theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:31
BanditRLProof.Exp3.mixedSquaredEstimatorCenteredSecondMoment_nonneg theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:58
BanditRLProof.Exp3.mixedSquaredEstimatorCenteredSecondMoment_le_card_div_floor theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:68
BanditRLProof.Exp3.integral_sq_mixedSquaredEstimatorDeviation_finiteActionMeasure_eq theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:84
BanditRLProof.Exp3.mixedSquaredEstimatorDeviation_condExpKernel_map_eq_finiteActionMeasure_of_condDistrib theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:105
BanditRLProof.Exp3.integral_sq_mixedSquaredEstimatorDeviation_condExpKernel_eq_of_condDistrib theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:219
BanditRLProof.Exp3.sampledTrajectoryPredictableMixedSquaredVarianceAt definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:300
BanditRLProof.Exp3.measurable_sampledTrajectoryPredictableMixedSquaredVarianceAt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:310
BanditRLProof.Exp3.sampledTrajectoryPredictableMixedSquaredVarianceAt_nonneg theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:330
BanditRLProof.Exp3.sampledTrajectoryPredictableMixedSquaredVarianceAt_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:348
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_zero_condExpKernel_integral_sq_eq_variance theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:373
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_succ_condExpKernel_integral_sq_eq_variance theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:436
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceProcess definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:500
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviationProcess_condExpKernel_integral_sq_eq_varianceProcess theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:515
BanditRLProof.Exp3.measurable_sampledTrajectoryPredictableMixedSquaredVarianceAt_filtration theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:559
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceProcess_isPredictable theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:620
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceProcess_sum_range_succ theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:640
BanditRLProof.Exp3.sampledPredictableMixedSquaredVariance_sum_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVariance Compiled BanditRLProof/Exp3MixedSquarePredictableVariance.lean:660
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_predictableVariance_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceHighProbabilityRegret.lean:21
BanditRLProof.Exp3.sampledPredictableVarianceSquareHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceHighProbabilityRegret.lean:80
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareHighProbabilityRegret_tail_joint theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceHighProbabilityRegret.lean:97
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceHighProbabilityRegret.lean:281
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareHighProbabilityRegret_tail_joint_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceHighProbabilityRegret.lean:365
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceHighProbabilityRegret.lean:413
BanditRLProof.Exp3.sum_prob_mul_sq_mixedSquaredEstimatorDeviation_le_inv_floor_mul_sum_loss_sq theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret.lean:19
BanditRLProof.Exp3.mixedSquaredEstimatorCenteredSecondMoment_le_inv_floor_mul_sum_loss_sq theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret.lean:92
BanditRLProof.Exp3.sampledTrajectoryPredictableMixedSquaredVarianceAt_le_inv_floor_mul_lossSquaredAt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret.lean:108
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceSum_le_inv_floor_mul_lossSquaredSum theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret.lean:134
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceLIntegral_le_of_lossSquaredSum_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret.lean:169
BanditRLProof.Exp3.sampledPredictableVarianceSquareLossEnergyRealizedMarkovHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret.lean:215
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareLossEnergyRealizedMarkovHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceLossEnergyRealizedMarkovHighProbabilityRegret.lean:225
BanditRLProof.Exp3.sampledPredictableDoubleVarianceRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedDoublePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedDoublePredictableVarianceHighProbabilityRegret.lean:19
BanditRLProof.Exp3.sampledPredictable_doublePredictableVarianceRealizedHighProbabilityRegret_tail_joint theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedDoublePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedDoublePredictableVarianceHighProbabilityRegret.lean:31
BanditRLProof.Exp3.sampledPredictableVarianceSquareRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret.lean:20
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareRealizedHighProbabilityRegret_tail_joint theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret.lean:30
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareRealizedHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret.lean:169
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareRealizedHighProbabilityRegret_tail_joint_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret.lean:255
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareRealizedHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedHighProbabilityRegret.lean:307
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceSum definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret.lean:20
BanditRLProof.Exp3.measurable_sampledPredictableMixedSquaredVarianceSum theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret.lean:30
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceSum_nonneg theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret.lean:45
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceLIntegral definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret.lean:62
BanditRLProof.Exp3.measure_sampledPredictableMixedSquaredVarianceSum_gt_le_lintegral_div theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret.lean:74
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareRealizedHighProbabilityRegret_tail_of_lintegral_variance_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret.lean:118
BanditRLProof.Exp3.sampledPredictableVarianceSquareRealizedMarkovHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret.lean:191
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareRealizedMarkovHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceRealizedMarkovHighProbabilityRegret.lean:201
BanditRLProof.Exp3.sampledPredictableVarianceSquareSmallLossDoubleVarianceRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedDoublePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedDoublePredictableVarianceHighProbabilityRegret.lean:20
BanditRLProof.Exp3.sampledPredictable_smallLossDoublePredictableVarianceRealizedHighProbabilityRegret_tail_joint_off_bad_of_lossMassSum_le_or_mem theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedDoublePredictableVarianceHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedDoublePredictableVarianceHighProbabilityRegret.lean:33
BanditRLProof.Exp3.predictableLossAt_mem_unitInterval theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:20
BanditRLProof.Exp3.sampledPredictableLossMassSum definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:36
BanditRLProof.Exp3.sampledPredictableLossSquaredAt_le_lossMassAt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:45
BanditRLProof.Exp3.sampledPredictableLossSquaredSum_le_lossMassSum theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:63
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceSum_le_inv_floor_mul_lossMassSum theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:76
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceLIntegral_le_of_lossMassSum_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:102
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_predictableVariance_off_bad_of_lossMassSum_le_or_mem theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:150
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_predictableVariance_of_lossMassSum_le_or_mem theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:233
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_predictableVariance_of_lossMassSum_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:316
BanditRLProof.Exp3.sampledPredictableVarianceSquareSmallLossHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:353
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareSmallLossHighProbabilityRegret_tail_joint_off_bad_of_lossMassSum_le_or_mem theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:371
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareSmallLossHighProbabilityRegret_tail_joint_of_lossMassSum_le_or_mem theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:559
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareSmallLossHighProbabilityRegret_tail_joint theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:763
BanditRLProof.Exp3.sampledPredictableVarianceSquareSmallLossRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:810
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareSmallLossRealizedHighProbabilityRegret_tail_joint_off_bad_of_lossMassSum_le_or_mem theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:822
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareSmallLossRealizedHighProbabilityRegret_tail_joint_of_lossMassSum_le_or_mem theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:960
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareSmallLossRealizedHighProbabilityRegret_tail_joint theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:1113
BanditRLProof.Exp3.sampledPredictableVarianceSquareSmallLossRealizedMarkovHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:1163
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareSmallLossRealizedMarkovHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSmallLossRealizedMarkovHighProbabilityRegret.lean:1174
BanditRLProof.Exp3.sampledPredictableSparseRealizedVarianceBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity.lean:20
BanditRLProof.Exp3.sampledPredictableRealizedVarianceSum_le_sparseRealizedVarianceBudget_or_mem_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity.lean:24
BanditRLProof.Exp3.sampledPredictableDoubleVarianceProbabilisticSparseLossRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity.lean:52
BanditRLProof.Exp3.sampledPredictable_doubleVarianceProbabilisticSparseLossRealizedHighProbabilityRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity.lean:64
BanditRLProof.Exp3.sampledPredictable_doubleVarianceProbabilisticSparseLossRealizedHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity.lean:214
BanditRLProof.Exp3.sampledPredictable_doubleVarianceProbabilisticSparseLossRealizedHighProbabilityRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsity.lean:271
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossLargeHorizonCondition definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon.lean:25
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon.lean:34
BanditRLProof.Exp3.sampledPredictable_allHorizonDoubleVarianceProbabilisticSparseLossRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon.lean:50
BanditRLProof.Exp3.sampledPredictable_allHorizonDoubleVarianceProbabilisticSparseLossRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon.lean:133
BanditRLProof.Exp3.sampledPredictable_allHorizonDoubleVarianceProbabilisticSparseLossRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityAllHorizon.lean:215
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossBestArmAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:21
BanditRLProof.Exp3.sampledPredictable_allHorizonDoubleVarianceProbabilisticSparseLossBestArmRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:29
BanditRLProof.Exp3.sampledPredictable_allHorizonDoubleVarianceProbabilisticSparseLossBestArmRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:178
BanditRLProof.Exp3.sampledPredictable_allHorizonDoubleVarianceProbabilisticSparseLossBestArmRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:275
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossRealizedExplorationScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:27
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossRawExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:33
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossClippedExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:41
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossClippedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:46
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossClippedExplorationRate_eq_raw theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:53
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossRawExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:65
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossClippedExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:73
BanditRLProof.Exp3.boundedRealizedLargeHorizon_of_doubleVarianceLargeHorizon theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:86
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossRawExplorationRate_le_half_of_horizon_contracts theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:106
BanditRLProof.Exp3.doubleVarianceProbabilisticSparseLossClippedExplorationRate_contracts theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:144
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossDoubleVarianceRealizedExplicitThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:267
BanditRLProof.Exp3.sparseRealizedPredictableVarianceRadius_le_three_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:274
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossDoubleVarianceRealizedTunedThreshold_le_explicitThreshold theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:321
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedDoubleVarianceProbabilisticSparseLossRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:419
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedDoubleVarianceProbabilisticSparseLossRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:505
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedDoubleVarianceProbabilisticSparseLossRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:564
BanditRLProof.Exp3.sampledPredictable_explicitDoubleVarianceProbabilisticSparseLossRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:620
BanditRLProof.Exp3.sampledPredictable_explicitDoubleVarianceProbabilisticSparseLossRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:697
BanditRLProof.Exp3.sampledPredictable_explicitDoubleVarianceProbabilisticSparseLossRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityExplicitTuning.lean:774
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossDoubleVarianceRealizedTunedThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning.lean:20
BanditRLProof.Exp3.sampledPredictableDoubleVarianceProbabilisticSparseLossRealizedHighProbabilityRegretBudget_le_tunedThreshold theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning.lean:39
BanditRLProof.Exp3.sampledPredictable_tunedDoubleVarianceProbabilisticSparseLossRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning.lean:67
BanditRLProof.Exp3.sampledPredictable_tunedDoubleVarianceProbabilisticSparseLossRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning.lean:150
BanditRLProof.Exp3.sampledPredictable_tunedDoubleVarianceProbabilisticSparseLossRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedDoublePathwiseVarianceProbabilisticSparsityTuning.lean:204
BanditRLProof.Exp3.sampledPredictable_allHorizonSparseLossPredictableVarianceRealizedMarkovRegret_tail_of_ae_sparsity theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovAESparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovAESparsityAllHorizon.lean:27
BanditRLProof.Exp3.sparseLossPredictableVarianceLargeHorizonCondition definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovAllHorizon.lean:25
BanditRLProof.Exp3.sparseLossPredictableVarianceAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovAllHorizon.lean:37
BanditRLProof.Exp3.sampledPredictable_allHorizonSparseLossPredictableVarianceRealizedMarkovRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovAllHorizon.lean:54
BanditRLProof.Exp3.log_one_div_fifth_eq_log_five_div theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:31
BanditRLProof.Exp3.sparseLossPredictableVarianceBudget_eq theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:38
BanditRLProof.Exp3.log_mul_sparseLossPredictableVarianceRadius_le_three_mul_sq_mul_horizon_sq theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:52
BanditRLProof.Exp3.sparseLossPredictableVarianceBalancedSqrt_le_two_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:175
BanditRLProof.Exp3.sparseLossPredictableVarianceRealizedMarkovExplicitThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:242
BanditRLProof.Exp3.sparseLossPredictableVarianceRealizedMarkovTunedThreshold_le_explicitThreshold theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:249
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedSparseLossPredictableVarianceRealizedMarkovRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:345
BanditRLProof.Exp3.sparseLossPredictableVarianceArmExplorationScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:429
BanditRLProof.Exp3.sparseLossPredictableVarianceMarkovExplorationScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:434
BanditRLProof.Exp3.sparseLossPredictableVarianceConfidenceExplorationScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:440
BanditRLProof.Exp3.sparseLossPredictableVarianceRealizedExplorationScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:445
BanditRLProof.Exp3.sparseLossPredictableVarianceRawExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:452
BanditRLProof.Exp3.sparseLossPredictableVarianceClippedExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:460
BanditRLProof.Exp3.rpow_inv_five_le_half_of_thirtytwo_mul_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:467
BanditRLProof.Exp3.numerator_le_pow_five_mul_of_rpow_inv_five_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:485
BanditRLProof.Exp3.sparseLossPredictableVarianceClippedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:506
BanditRLProof.Exp3.sparseLossPredictableVarianceClippedExplorationRate_eq_raw theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:512
BanditRLProof.Exp3.sparseLossPredictableVarianceRawExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:520
BanditRLProof.Exp3.sparseLossPredictableVarianceClippedExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:530
BanditRLProof.Exp3.sparseLossPredictableVarianceRawExplorationRate_le_half_of_horizon_contracts theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:540
BanditRLProof.Exp3.sparseLossPredictableVarianceClippedExplorationRate_contracts theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:582
BanditRLProof.Exp3.sampledPredictable_explicitSparseLossPredictableVarianceRealizedMarkovRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovExplicitTuning.lean:688
BanditRLProof.Exp3.sampledPredictableLossSupport definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret.lean:29
BanditRLProof.Exp3.sampledPredictableLossMassAt_le_supportCard theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret.lean:39
BanditRLProof.Exp3.sampledPredictableLossMassSum_le_sparsity_mul_horizon_of_sample theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret.lean:69
BanditRLProof.Exp3.sampledPredictableLossMassSum_le_sparsity_mul_horizon theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret.lean:94
BanditRLProof.Exp3.sampledPredictableVarianceSquareSparseLossRealizedMarkovHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret.lean:108
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareSparseLossRealizedMarkovHighProbabilityRegret_tail_total_delta_of_ae_sparsity theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret.lean:118
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareSparseLossRealizedMarkovHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovHighProbabilityRegret.lean:169
BanditRLProof.Exp3.sampledPredictableSparsityFailure definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity.lean:26
BanditRLProof.Exp3.sampledPredictableLossMassSum_le_or_mem_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity.lean:37
BanditRLProof.Exp3.sampledPredictableLossMassSum_le_card_mul_horizon theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity.lean:59
BanditRLProof.Exp3.sampledPredictableGlobalVarianceMeanBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity.lean:73
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceLIntegral_le_globalLossMass theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity.lean:81
BanditRLProof.Exp3.sampledPredictableVarianceSquareProbabilisticSparseLossRealizedMarkovHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity.lean:107
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareProbabilisticSparseLossRealizedMarkovHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity.lean:119
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareProbabilisticSparseLossRealizedMarkovHighProbabilityRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsity.lean:272
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceLargeHorizonCondition definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityAllHorizon.lean:31
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityAllHorizon.lean:42
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPredictableVarianceRealizedMarkovRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityAllHorizon.lean:58
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPredictableVarianceRealizedMarkovRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityAllHorizon.lean:140
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceBudget_eq theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:31
BanditRLProof.Exp3.log_mul_probabilisticSparseLossPredictableVarianceRadius_le_three_mul_sq_mul_horizon_sq theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:48
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceBalancedSqrt_le_two_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:172
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceRealizedMarkovExplicitThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:240
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceRealizedMarkovTunedThreshold_le_explicitThreshold theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:247
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedProbabilisticSparseLossPredictableVarianceRealizedMarkovRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:344
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedProbabilisticSparseLossPredictableVarianceRealizedMarkovRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:434
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceMarkovExplorationScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:490
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceRawExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:497
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceClippedExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:509
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceClippedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:515
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceClippedExplorationRate_eq_raw theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:522
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceRawExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:534
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceClippedExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:546
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceRawExplorationRate_le_half_of_horizon_contracts theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:559
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceClippedExplorationRate_contracts theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:602
BanditRLProof.Exp3.sampledPredictable_explicitProbabilisticSparseLossPredictableVarianceRealizedMarkovRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:728
BanditRLProof.Exp3.sampledPredictable_explicitProbabilisticSparseLossPredictableVarianceRealizedMarkovRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityExplicitTuning.lean:805
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:29
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceBudget_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:35
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceHighProbabilityScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:57
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceHighProbabilityScale_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:67
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceHighProbabilityLearningRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:96
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceHighProbabilityLearningRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:105
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceHighProbabilityLearningRate_sq_mul_scale theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:121
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceHighProbabilityHedgeBudget_le_three_mul_sqrt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:144
BanditRLProof.Exp3.probabilisticSparseLossPredictableVarianceRealizedMarkovTunedThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:224
BanditRLProof.Exp3.sampledPredictableVarianceSquareProbabilisticSparseLossRealizedMarkovHighProbabilityRegretBudget_le_tunedThreshold theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:241
BanditRLProof.Exp3.sampledPredictable_tunedProbabilisticSparseLossPredictableVarianceRealizedMarkovRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:270
BanditRLProof.Exp3.sampledPredictable_tunedProbabilisticSparseLossPredictableVarianceRealizedMarkovRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovProbabilisticSparsityTuning.lean:357
BanditRLProof.Exp3.sparseLossPredictableVarianceBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:32
BanditRLProof.Exp3.sparseLossPredictableVarianceBudget_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:38
BanditRLProof.Exp3.sparseLossPredictableVarianceHighProbabilityScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:56
BanditRLProof.Exp3.sparseLossPredictableVarianceHighProbabilityScale_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:66
BanditRLProof.Exp3.sparseLossPredictableVarianceHighProbabilityLearningRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:100
BanditRLProof.Exp3.sparseLossPredictableVarianceHighProbabilityLearningRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:109
BanditRLProof.Exp3.sparseLossPredictableVarianceHighProbabilityLearningRate_sq_mul_scale theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:126
BanditRLProof.Exp3.sparseLossPredictableVarianceHighProbabilityHedgeBudget_le_three_mul_sqrt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:150
BanditRLProof.Exp3.sparseLossPredictableVarianceRealizedMarkovTunedThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:229
BanditRLProof.Exp3.sampledPredictableVarianceSquareSparseLossRealizedMarkovHighProbabilityRegretBudget_le_tunedThreshold theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:246
BanditRLProof.Exp3.sampledPredictable_tunedSparseLossPredictableVarianceRealizedMarkovRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedMarkovTuning.lean:276
BanditRLProof.Exp3.sampledPredictableSparsePathwiseVarianceBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity.lean:27
BanditRLProof.Exp3.sampledPredictableMixedSquaredVarianceSum_le_sparsePathwiseVarianceBudget_or_mem_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity.lean:35
BanditRLProof.Exp3.sampledPredictableVarianceSquareProbabilisticSparseLossRealizedPathwiseVarianceHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity.lean:65
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareProbabilisticSparseLossRealizedPathwiseVarianceHighProbabilityRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity.lean:78
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareProbabilisticSparseLossRealizedPathwiseVarianceHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity.lean:199
BanditRLProof.Exp3.sampledPredictable_predictableVarianceSquareProbabilisticSparseLossRealizedPathwiseVarianceHighProbabilityRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsity.lean:258
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossLargeHorizonCondition definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon.lean:30
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon.lean:41
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon.lean:58
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon.lean:141
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityAllHorizon.lean:223
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossBestArmAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:26
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPathwiseVarianceBestArmRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:34
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPathwiseVarianceBestArmRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:184
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPathwiseVarianceBestArmRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:334
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPathwiseVarianceBestArmRealizedRegret_tail_single_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:428
BanditRLProof.Exp3.sampledPredictable_allHorizonProbabilisticSparseLossPathwiseVarianceBestArmRealizedRegret_tail_of_sparsityFailure_le_single_charge theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityBestArmAllHorizon.lean:525
BanditRLProof.Exp3.sampledPredictableSparsePathwiseVarianceBudget_eq theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:34
BanditRLProof.Exp3.log_mul_pathwiseVarianceProbabilisticSparseLossRadius_le_three_mul_sq_mul_horizon_sq theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:49
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossBalancedSqrt_le_two_mul_gamma_mul_horizon theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:172
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossRealizedExplicitThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:239
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossRealizedTunedThreshold_le_explicitThreshold theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:246
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:343
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:430
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:510
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossMixedExplorationScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:567
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossRawExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:574
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossClippedExplorationRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:586
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossClippedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:591
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossClippedExplorationRate_eq_raw theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:598
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossRawExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:610
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossClippedExplorationRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:622
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossRawExplorationRate_le_half_of_horizon_contracts theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:635
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossClippedExplorationRate_contracts theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:677
BanditRLProof.Exp3.sampledPredictable_explicitProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:798
BanditRLProof.Exp3.sampledPredictable_explicitProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:875
BanditRLProof.Exp3.sampledPredictable_explicitProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityExplicitTuning.lean:952
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossHighProbabilityScale definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:25
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossHighProbabilityScale_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:35
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossHighProbabilityLearningRate definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:73
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossHighProbabilityLearningRate_pos theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:82
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossHighProbabilityLearningRate_sq_mul_scale theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:98
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossHighProbabilityHedgeBudget_le_three_mul_sqrt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:121
BanditRLProof.Exp3.pathwiseVarianceProbabilisticSparseLossRealizedTunedThreshold definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:200
BanditRLProof.Exp3.sampledPredictableVarianceSquareProbabilisticSparseLossRealizedPathwiseVarianceHighProbabilityRegretBudget_le_tunedThreshold theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:216
BanditRLProof.Exp3.sampledPredictable_tunedProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail_off_sparsityFailure theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:244
BanditRLProof.Exp3.sampledPredictable_tunedProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:328
BanditRLProof.Exp3.sampledPredictable_tunedProbabilisticSparseLossPathwiseVarianceRealizedRegret_tail_of_sparsityFailure_le theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceSparseLossRealizedPathwiseVarianceProbabilisticSparsityTuning.lean:392
BanditRLProof.Exp3.abs_mixedSquaredEstimatorDeviation_le_inv_floor theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:21
BanditRLProof.Exp3.finiteActionMixedSquaredEstimator_hasMGFUpperBoundAt_variance theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:87
BanditRLProof.Exp3.finiteActionMixedSquaredEstimator_compensated_hasMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:179
BanditRLProof.Exp3.mixedSquaredEstimator_compensated_hasCondMGFUpperBoundAt_of_condDistrib theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:206
BanditRLProof.Exp3.sampledPredictableMixedSquaredCompensated_zero_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:405
BanditRLProof.Exp3.sampledPredictableMixedSquaredCompensated_succ_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:465
BanditRLProof.Exp3.sampledPredictableMixedSquaredCompensatedProcess definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:527
BanditRLProof.Exp3.sampledPredictableMixedSquaredCompensatedProcess_stronglyAdapted theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:539
BanditRLProof.Exp3.sampledPredictableMixedSquaredCompensatedProcess_sum_range_succ theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:561
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_sum_tail_predictableVariance_fixedTilt theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:585
BanditRLProof.Exp3.sampledMixedSquaredPredictableVarianceRadius definition EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:714
BanditRLProof.Exp3.sampledPredictableMixedSquaredDeviation_sum_tail_predictableVariance_delta theorem EXP3 BanditRLProof.Exp3MixedSquarePredictableVarianceTail Compiled BanditRLProof/Exp3MixedSquarePredictableVarianceTail.lean:725
BanditRLProof.Exp3Potential.potential definition EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:20
BanditRLProof.Exp3Potential.updatedWeight definition EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:25
BanditRLProof.Exp3Potential.updatedPotential definition EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:30
BanditRLProof.Exp3Potential.updatedPotential_eq_sum theorem EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:36
BanditRLProof.Exp3Potential.updatedWeight_nonneg_of_nonneg theorem EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:44
BanditRLProof.Exp3Potential.updatedPotential_nonneg_of_nonneg theorem EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:51
BanditRLProof.Exp3Potential.updatedPotential_sub_potential_eq_sum_weight_mul_exp_sub_one theorem EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:65
BanditRLProof.Exp3Potential.sum_range_forward_difference theorem EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:78
BanditRLProof.Exp3Potential.potentialProcess definition EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:90
BanditRLProof.Exp3Potential.potentialProcess_telescope_sum_range theorem EXP3 BanditRLProof.Exp3Potential Compiled BanditRLProof/Exp3Potential.lean:100
BanditRLProof.Exp3.PredictableLossVector structure EXP3 BanditRLProof.Exp3PredictableAdversary Compiled BanditRLProof/Exp3PredictableAdversary.lean:24
BanditRLProof.Exp3.PredictableLossVector.environment definition EXP3 BanditRLProof.Exp3PredictableAdversary Compiled BanditRLProof/Exp3PredictableAdversary.lean:43
BanditRLProof.Exp3.PredictableLossVector.environment_initialFeedback_apply theorem EXP3 BanditRLProof.Exp3PredictableAdversary Compiled BanditRLProof/Exp3PredictableAdversary.lean:57
BanditRLProof.Exp3.PredictableLossVector.environment_feedback_apply theorem EXP3 BanditRLProof.Exp3PredictableAdversary Compiled BanditRLProof/Exp3PredictableAdversary.lean:66
BanditRLProof.Exp3.PredictableLossVector.initial_mem_unitInterval theorem EXP3 BanditRLProof.Exp3PredictableAdversary Compiled BanditRLProof/Exp3PredictableAdversary.lean:76
BanditRLProof.Exp3.PredictableLossVector.successor_mem_unitInterval theorem EXP3 BanditRLProof.Exp3PredictableAdversary Compiled BanditRLProof/Exp3PredictableAdversary.lean:83
BanditRLProof.Exp3.trajectoryMixture_condDistrib_action_given_environment_history theorem EXP3 BanditRLProof.Exp3PredictableAdversary Compiled BanditRLProof/Exp3PredictableAdversary.lean:96
BanditRLProof.Exp3.sampledImportanceWeightedTrajectoryMeasure_condDistrib_action_given_environment theorem EXP3 BanditRLProof.Exp3PredictableAdversary Compiled BanditRLProof/Exp3PredictableAdversary.lean:219
BanditRLProof.Exp3.sampledPredictableTrajectoryMeasure_reward_nonneg_ae theorem EXP3 BanditRLProof.Exp3PredictableHedge Compiled BanditRLProof/Exp3PredictableHedge.lean:26
BanditRLProof.Exp3.sampledPredictableTrajectoryMeasure_finiteHorizon_reward_nonneg_ae theorem EXP3 BanditRLProof.Exp3PredictableHedge Compiled BanditRLProof/Exp3PredictableHedge.lean:71
BanditRLProof.Exp3.sampledPredictableTrajectoryMeasure_hedge_regret_le_ae theorem EXP3 BanditRLProof.Exp3PredictableHedge Compiled BanditRLProof/Exp3PredictableHedge.lean:96
BanditRLProof.Exp3.sampledPredictableScoreHedge_ae theorem EXP3 BanditRLProof.Exp3PredictableHedge Compiled BanditRLProof/Exp3PredictableHedge.lean:130
BanditRLProof.Exp3.sampledTrajectoryPureProbabilityAt definition EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:25
BanditRLProof.Exp3.sampledTrajectoryPureProbabilitySourceAt definition EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:34
BanditRLProof.Exp3.sampledTrajectoryPurePredictableLossAt definition EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:69
BanditRLProof.Exp3.sampledTrajectoryExploredPredictableLossAt definition EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:80
BanditRLProof.Exp3.sampledTrajectoryPureObservedLossAt definition EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:91
BanditRLProof.Exp3.measurable_sampledTrajectoryPurePredictableLossAt theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:98
BanditRLProof.Exp3.sampledTrajectoryPurePredictableLossAt_mem_unitInterval theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:114
BanditRLProof.Exp3.integrable_sampledTrajectoryPurePredictableLossAt theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:149
BanditRLProof.Exp3.measurable_sampledTrajectoryExploredPredictableLossAt theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:167
BanditRLProof.Exp3.sampledTrajectoryExploredPredictableLossAt_mem_unitInterval theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:185
BanditRLProof.Exp3.integrable_sampledTrajectoryExploredPredictableLossAt theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:222
BanditRLProof.Exp3.sampledTrajectoryPureObservedLossAt_ae_eq_weightedPredictable theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:244
BanditRLProof.Exp3.integrable_sampledTrajectoryPureObservedLossAt theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:303
BanditRLProof.Exp3.sampledPredictablePureObservedInitial_integral_eq theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:346
BanditRLProof.Exp3.sampledPredictablePureObservedSuccessor_integral_eq theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:475
BanditRLProof.Exp3.sampledPredictablePureObservedAt_integral_eq theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:627
BanditRLProof.Exp3.sampledPredictablePureObserved_finiteHorizon_integral_eq theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:652
BanditRLProof.Exp3.sampledPredictableTrajectoryMeasure_hedge_exploredSecondMoment_le_ae theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:703
BanditRLProof.Exp3.sampledPredictable_integral_pureHedge_le_exploredSecondMoment theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:763
BanditRLProof.Exp3.sampledPredictable_integral_exploredLoss_le_pure_add_gamma theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:838
BanditRLProof.Exp3.sampledPredictableObserved_finiteHorizon_secondMoment_integral_le_card_mul theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:907
BanditRLProof.Exp3.sampledPredictable_expectedRegret_le theorem EXP3 BanditRLProof.Exp3PredictableIntegration Compiled BanditRLProof/Exp3PredictableIntegration.lean:978
BanditRLProof.Exp3.trajectoryMixture_map_environment_history_output_eq_compProd theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:24
BanditRLProof.Exp3.canonicalMeasurableEnvironmentTrajectoryMeasure_map_environment_prefix_next_eq_compProd theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:150
BanditRLProof.Exp3.canonicalMeasurableEnvironmentTrajectoryMeasure_condDistrib_nextPair_given_environment_prefix theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:190
BanditRLProof.Exp3.sampledEnvironmentHistoryDistributionSource definition EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:223
BanditRLProof.Exp3.sampledPredictableSuccessorLossRegularity theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:251
BanditRLProof.Exp3.sampledInitialEnvironmentDistributionSource definition EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:278
BanditRLProof.Exp3.sampledPredictableInitialLossRegularity theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:292
BanditRLProof.Exp3.canonicalMeasurableEnvironmentTrajectoryMeasure_map_environment_eval_zero theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:315
BanditRLProof.Exp3.canonicalMeasurableEnvironmentTrajectoryMeasure_map_environment_action_zero theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:347
BanditRLProof.Exp3.canonicalMeasurableEnvironmentTrajectoryMeasure_condDistrib_action_zero_given_environment theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:389
BanditRLProof.Exp3.canonicalPredictableTrajectoryMeasure_reward_zero_eq_initialLoss_ae theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:446
BanditRLProof.Exp3.sampledPredictableObservedInitial_first_second_moment theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:513
BanditRLProof.Exp3.canonicalPredictableTrajectoryMeasure_reward_eq_successorLoss_ae theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:675
BanditRLProof.Exp3.sampledPredictableTrajectoryMeasure_reward_eq_successorLoss_ae theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:758
BanditRLProof.Exp3.sampledPredictableSuccessorLoss_first_second_moment theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:787
BanditRLProof.Exp3.sampledPredictableObservedSuccessor_first_second_moment theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:914
BanditRLProof.Exp3.sampledTrajectoryProbabilityAt definition EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1008
BanditRLProof.Exp3.predictableLossAt definition EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1018
BanditRLProof.Exp3.observedImportanceWeightedLossAt definition EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1029
BanditRLProof.Exp3.observedMixedSquaredImportanceWeightedLossAt definition EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1038
BanditRLProof.Exp3.sampledTrajectoryProbabilitySourceAt definition EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1047
BanditRLProof.Exp3.sampledPredictableTrajectoryLossRegularityAt theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1078
BanditRLProof.Exp3.measurable_predictableLossAt theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1128
BanditRLProof.Exp3.measurable_observedImportanceWeightedLossAt theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1146
BanditRLProof.Exp3.measurable_observedMixedSquaredImportanceWeightedLossAt theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1164
BanditRLProof.Exp3.integrable_predictableImportanceWeightedLossAt theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1184
BanditRLProof.Exp3.integrable_predictableMixedSquaredImportanceWeightedLossAt theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1217
BanditRLProof.Exp3.integrable_predictableLossAt theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1249
BanditRLProof.Exp3.integrable_predictableLossSqSumAt theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1269
BanditRLProof.Exp3.observedAt_eq_predictableAt_ae theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1297
BanditRLProof.Exp3.integrable_observedAt theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1375
BanditRLProof.Exp3.sampledPredictableObservedAt_first_second_moment theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1408
BanditRLProof.Exp3.sampledPredictableObserved_finiteHorizon_first_second_moment theorem EXP3 BanditRLProof.Exp3PredictableMoments Compiled BanditRLProof/Exp3PredictableMoments.lean:1553
BanditRLProof.Exp3.sampledPredictableRegretGeometricAllTimeBudget definition EXP3 BanditRLProof.Exp3PredictableRegretAllTime Compiled BanditRLProof/Exp3PredictableRegretAllTime.lean:24
BanditRLProof.Exp3.sampledPredictableRegretGeometricAllTimeFailureSet definition EXP3 BanditRLProof.Exp3PredictableRegretAllTime Compiled BanditRLProof/Exp3PredictableRegretAllTime.lean:32
BanditRLProof.Exp3.mem_sampledPredictableRegretGeometricAllTimeFailureSet_iff theorem EXP3 BanditRLProof.Exp3PredictableRegretAllTime Compiled BanditRLProof/Exp3PredictableRegretAllTime.lean:49
BanditRLProof.Exp3.measure_sampledPredictableRegretGeometricAllTimeFailureSet_le theorem EXP3 BanditRLProof.Exp3PredictableRegretAllTime Compiled BanditRLProof/Exp3PredictableRegretAllTime.lean:70
BanditRLProof.Exp3.weightedImportanceWeightedLoss_eq_selected theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:22
BanditRLProof.Exp3.sum_prob_mul_sq_weightedEstimatorMeanMinusRaw_le_inv_floor theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:38
BanditRLProof.Exp3.finiteActionWeightedEstimatorMeanMinusRaw_hasMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:118
BanditRLProof.Exp3.weightedEstimatorMeanMinusRaw_hasCondMGFUpperBoundAt_of_condDistrib_ae_eq_finiteActionKernel theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:260
BanditRLProof.Exp3.sampledTrajectoryPurePredictableMinusWeightedAt definition EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:412
BanditRLProof.Exp3.sampledPurePredictableMinusWeighted_zero_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:424
BanditRLProof.Exp3.sampledPurePredictableMinusWeighted_succ_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:488
BanditRLProof.Exp3.sampledPurePredictableMinusObserved_zero_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:565
BanditRLProof.Exp3.sampledPurePredictableMinusObserved_succ_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:625
BanditRLProof.Exp3.sampledPurePredictableMinusObserved_sum_tail_fixedTilt theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:696
BanditRLProof.Exp3.sampledPurePredictableMinusObservedBernsteinConfidenceRadius definition EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:773
BanditRLProof.Exp3.sampledPurePredictableMinusObserved_sum_tail_bernstein_delta theorem EXP3 BanditRLProof.Exp3PureBernstein Compiled BanditRLProof/Exp3PureBernstein.lean:783
BanditRLProof.Exp3.weightedEstimator_hasCondSubgaussianMGF_of_condDistrib_ae_eq_finiteActionKernel theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:24
BanditRLProof.Exp3.sampledTrajectoryWeightedPurePredictableDeviationAt definition EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:193
BanditRLProof.Exp3.sampledTrajectoryPureObservedDeviationAt definition EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:205
BanditRLProof.Exp3.sampledWeightedPurePredictableDeviation_zero_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:214
BanditRLProof.Exp3.sampledWeightedPurePredictableDeviation_succ_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:275
BanditRLProof.Exp3.sampledPureObservedDeviation_zero_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:349
BanditRLProof.Exp3.sampledPureObservedDeviation_succ_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:404
BanditRLProof.Exp3.sampledPureObservedDeviationProcess definition EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:467
BanditRLProof.Exp3.sampledPureObservedDeviationProcess_stronglyAdapted theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:477
BanditRLProof.Exp3.sampledPureObservedDeviationVarianceProxy abbreviation EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:668
BanditRLProof.Exp3.sampledPureObservedDeviationProxy abbreviation EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:672
BanditRLProof.Exp3.sampledPureObservedDeviationProcess_sum_range_succ theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:676
BanditRLProof.Exp3.sampledPureObservedDeviation_sum_tail_ennreal theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:713
BanditRLProof.Exp3.sampledPureObservedDeviationConfidenceRadius definition EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:784
BanditRLProof.Exp3.sampledPureObservedDeviation_sum_tail_exp_neg_budget theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:792
BanditRLProof.Exp3.sampledPureObservedDeviation_sum_tail_delta theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:841
BanditRLProof.Exp3.sampledTrajectoryPurePredictableMinusObservedAt definition EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:879
BanditRLProof.Exp3.sampledPurePredictableMinusObserved_zero_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:888
BanditRLProof.Exp3.sampledPurePredictableMinusObserved_succ_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:917
BanditRLProof.Exp3.sampledPurePredictableMinusObservedProcess definition EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:949
BanditRLProof.Exp3.sampledPurePredictableMinusObservedProcess_stronglyAdapted theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:960
BanditRLProof.Exp3.sampledPurePredictableMinusObservedProcess_sum_range_succ theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:987
BanditRLProof.Exp3.sampledPurePredictableMinusObserved_sum_tail_ennreal theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:1027
BanditRLProof.Exp3.sampledPurePredictableMinusObserved_sum_tail_exp_neg_budget theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:1098
BanditRLProof.Exp3.sampledPurePredictableMinusObserved_sum_tail_delta theorem EXP3 BanditRLProof.Exp3PureConfidence Compiled BanditRLProof/Exp3PureConfidence.lean:1147
BanditRLProof.Exp3.randomSquareBernsteinLargeHorizonCondition definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedAllHorizon Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedAllHorizon.lean:22
BanditRLProof.Exp3.randomSquareBernsteinAllHorizonRegretThreshold definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedAllHorizon Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedAllHorizon.lean:30
BanditRLProof.Exp3.sampledPredictable_allHorizonRandomSquareBernsteinRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedAllHorizon Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedAllHorizon.lean:46
BanditRLProof.Exp3.log_one_div_fourth_eq_log_four_div theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:21
BanditRLProof.Exp3.randomSquareBernsteinRealizedExplicitThreshold definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:29
BanditRLProof.Exp3.randomSquareBernsteinRealizedTunedThreshold_le_explicitThreshold theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:40
BanditRLProof.Exp3.sampledPredictable_gammaCharacterizedRandomSquareBernsteinRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:114
BanditRLProof.Exp3.randomSquareBernsteinConfidenceExplorationScale definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:187
BanditRLProof.Exp3.randomSquareBernsteinRealizedExplorationScale definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:192
BanditRLProof.Exp3.randomSquareBernsteinRawExplorationRate definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:199
BanditRLProof.Exp3.randomSquareBernsteinClippedExplorationRate definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:205
BanditRLProof.Exp3.randomSquareBernsteinClippedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:209
BanditRLProof.Exp3.randomSquareBernsteinClippedExplorationRate_eq_raw theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:214
BanditRLProof.Exp3.randomSquareBernsteinRawExplorationRate_pos theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:221
BanditRLProof.Exp3.randomSquareBernsteinClippedExplorationRate_pos theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:235
BanditRLProof.Exp3.randomSquareBernsteinRawExplorationRate_le_half_of_horizon_contracts theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:245
BanditRLProof.Exp3.randomSquareBernsteinClippedExplorationRate_contracts theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:273
BanditRLProof.Exp3.sampledPredictable_explicitRandomSquareBernsteinRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedExplicitTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedExplicitTuning.lean:328
BanditRLProof.Exp3.sampledPredictableRandomSquareBernsteinRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedHighProbabilityRegret.lean:26
BanditRLProof.Exp3.sampledPredictable_randomSquareBernsteinRealizedHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedHighProbabilityRegret.lean:36
BanditRLProof.Exp3.sampledPredictable_randomSquareBernsteinRealizedHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedHighProbabilityRegret.lean:158
BanditRLProof.Exp3.randomSquareHighProbabilityLearningRate definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedTuning.lean:26
BanditRLProof.Exp3.randomSquareHighProbabilityLearningRate_pos theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedTuning.lean:30
BanditRLProof.Exp3.randomSquareHighProbabilityLearningRate_sq_mul theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedTuning.lean:37
BanditRLProof.Exp3.randomSquareHighProbabilityHedgeBudget_le_three_mul_sqrt theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedTuning.lean:47
BanditRLProof.Exp3.randomSquareBernsteinRealizedTunedThreshold definition EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedTuning.lean:113
BanditRLProof.Exp3.sampledPredictableRandomSquareBernsteinRealizedHighProbabilityRegretBudget_le_tunedThreshold theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedTuning.lean:128
BanditRLProof.Exp3.sampledPredictable_tunedRandomSquareBernsteinRealizedRegret_tail theorem EXP3 BanditRLProof.Exp3RandomSquareBernsteinRealizedTuning Compiled BanditRLProof/Exp3RandomSquareBernsteinRealizedTuning.lean:158
BanditRLProof.Exp3.sampledObservedMixedSquaredSum definition EXP3 BanditRLProof.Exp3RandomSquareHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareHighProbabilityRegret.lean:23
BanditRLProof.Exp3.observedMixedSquaredImportanceWeightedLossAt_nonneg theorem EXP3 BanditRLProof.Exp3RandomSquareHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareHighProbabilityRegret.lean:31
BanditRLProof.Exp3.sampledObservedMixedSquaredSum_nonneg theorem EXP3 BanditRLProof.Exp3RandomSquareHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareHighProbabilityRegret.lean:49
BanditRLProof.Exp3.measurable_sampledObservedMixedSquaredSum theorem EXP3 BanditRLProof.Exp3RandomSquareHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareHighProbabilityRegret.lean:62
BanditRLProof.Exp3.integrable_sampledPredictableObservedMixedSquaredSum theorem EXP3 BanditRLProof.Exp3RandomSquareHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareHighProbabilityRegret.lean:79
BanditRLProof.Exp3.sampledPredictableObservedMixedSquared_sum_tail_markov theorem EXP3 BanditRLProof.Exp3RandomSquareHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareHighProbabilityRegret.lean:108
BanditRLProof.Exp3.sampledPredictableRandomSquareBernsteinHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3RandomSquareHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareHighProbabilityRegret.lean:184
BanditRLProof.Exp3.sampledPredictable_randomSquareBernsteinHighProbabilityRegret_tail theorem EXP3 BanditRLProof.Exp3RandomSquareHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareHighProbabilityRegret.lean:198
BanditRLProof.Exp3.sampledPredictable_randomSquareBernsteinHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3RandomSquareHighProbabilityRegret Compiled BanditRLProof/Exp3RandomSquareHighProbabilityRegret.lean:359
BanditRLProof.Exp3.condExpKernel_map_eq_finiteActionMeasure_of_condDistrib_ae_eq theorem EXP3 BanditRLProof.Exp3RealizedConcentration Compiled BanditRLProof/Exp3RealizedConcentration.lean:20
BanditRLProof.Exp3.sampledTrajectorySelectedDeviationAt definition EXP3 BanditRLProof.Exp3RealizedConcentration Compiled BanditRLProof/Exp3RealizedConcentration.lean:180
BanditRLProof.Exp3.measurable_sampledTrajectorySelectedDeviationAt theorem EXP3 BanditRLProof.Exp3RealizedConcentration Compiled BanditRLProof/Exp3RealizedConcentration.lean:189
BanditRLProof.Exp3.sampledPredictableSelectedDeviation_succ_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3RealizedConcentration Compiled BanditRLProof/Exp3RealizedConcentration.lean:204
BanditRLProof.Exp3.sampledTrajectoryRealizedDeviationAt definition EXP3 BanditRLProof.Exp3RealizedConcentration Compiled BanditRLProof/Exp3RealizedConcentration.lean:367
BanditRLProof.Exp3.sampledPredictableRealizedDeviation_succ_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3RealizedConcentration Compiled BanditRLProof/Exp3RealizedConcentration.lean:376
BanditRLProof.Exp3.sampledPredictableRealizedDeviationConfidenceRadius definition EXP3 BanditRLProof.Exp3RealizedConfidence Compiled BanditRLProof/Exp3RealizedConfidence.lean:19
BanditRLProof.Exp3.intervalVarianceProxy_zero_one_pos theorem EXP3 BanditRLProof.Exp3RealizedConfidence Compiled BanditRLProof/Exp3RealizedConfidence.lean:26
BanditRLProof.Exp3.sampledPredictableRealizedDeviationConfidenceRadius_nonneg theorem EXP3 BanditRLProof.Exp3RealizedConfidence Compiled BanditRLProof/Exp3RealizedConfidence.lean:30
BanditRLProof.Exp3.sampledPredictableRealizedDeviationConfidenceRadius_sq_domination theorem EXP3 BanditRLProof.Exp3RealizedConfidence Compiled BanditRLProof/Exp3RealizedConfidence.lean:35
BanditRLProof.Exp3.sampledPredictableRealizedDeviation_sum_tail_exp_neg_budget theorem EXP3 BanditRLProof.Exp3RealizedConfidence Compiled BanditRLProof/Exp3RealizedConfidence.lean:45
BanditRLProof.Exp3.sampledPredictableRealizedDeviation_sum_tail_delta theorem EXP3 BanditRLProof.Exp3RealizedConfidence Compiled BanditRLProof/Exp3RealizedConfidence.lean:90
BanditRLProof.Exp3.sampledRealizedPredictableVarianceLinearBudget definition EXP3 BanditRLProof.Exp3RealizedDeviationAllTime Compiled BanditRLProof/Exp3RealizedDeviationAllTime.lean:19
BanditRLProof.Exp3.sampledRealizedPredictableVarianceLinearBudget_pos theorem EXP3 BanditRLProof.Exp3RealizedDeviationAllTime Compiled BanditRLProof/Exp3RealizedDeviationAllTime.lean:23
BanditRLProof.Exp3.sampledRealizedDeviationGeometricAllTimeRadius definition EXP3 BanditRLProof.Exp3RealizedDeviationAllTime Compiled BanditRLProof/Exp3RealizedDeviationAllTime.lean:30
BanditRLProof.Exp3.sampledRealizedDeviationGeometricAllTimeFailureSet definition EXP3 BanditRLProof.Exp3RealizedDeviationAllTime Compiled BanditRLProof/Exp3RealizedDeviationAllTime.lean:37
BanditRLProof.Exp3.mem_sampledRealizedDeviationGeometricAllTimeFailureSet_iff theorem EXP3 BanditRLProof.Exp3RealizedDeviationAllTime Compiled BanditRLProof/Exp3RealizedDeviationAllTime.lean:48
BanditRLProof.Exp3.sampledPredictableRealizedDeviationAllTimeFailureSet_linearBudget_eq theorem EXP3 BanditRLProof.Exp3RealizedDeviationAllTime Compiled BanditRLProof/Exp3RealizedDeviationAllTime.lean:65
BanditRLProof.Exp3.measure_sampledRealizedDeviationGeometricAllTimeFailureSet_le theorem EXP3 BanditRLProof.Exp3RealizedDeviationAllTime Compiled BanditRLProof/Exp3RealizedDeviationAllTime.lean:97
BanditRLProof.Exp3.sampledPredictableSelectedDeviation_zero_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:19
BanditRLProof.Exp3.sampledPredictableRealizedDeviation_zero_hasCondSubgaussianMGF theorem EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:178
BanditRLProof.Exp3.sampledPredictableDeviationFiltration definition EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:235
BanditRLProof.Exp3.sampledPredictableDeviationFiltration_zero theorem EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:312
BanditRLProof.Exp3.sampledPredictableDeviationFiltration_succ theorem EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:320
BanditRLProof.Exp3.sampledPredictableRealizedDeviationProcess definition EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:329
BanditRLProof.Exp3.sampledPredictableRealizedDeviationProxy definition EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:339
BanditRLProof.Exp3.sampledPredictableRealizedDeviationProcess_stronglyAdapted theorem EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:343
BanditRLProof.Exp3.sampledPredictableRealizedDeviationProcess_sum_range_succ theorem EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:476
BanditRLProof.Exp3.sampledPredictableRealizedDeviationProxy_sum_range_succ theorem EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:513
BanditRLProof.Exp3.sampledPredictableRealizedDeviation_sum_tail_ennreal theorem EXP3 BanditRLProof.Exp3RealizedDeviationTail Compiled BanditRLProof/Exp3RealizedDeviationTail.lean:530
BanditRLProof.Exp3.sampledPredictableRealizedHighProbabilityRegretBudget definition EXP3 BanditRLProof.Exp3RealizedHighProbabilityRegret Compiled BanditRLProof/Exp3RealizedHighProbabilityRegret.lean:24
BanditRLProof.Exp3.sampledPredictable_realizedHighProbabilityRegret_tail_delta theorem EXP3 BanditRLProof.Exp3RealizedHighProbabilityRegret Compiled BanditRLProof/Exp3RealizedHighProbabilityRegret.lean:35
BanditRLProof.Exp3.sampledPredictable_realizedHighProbabilityRegret_tail_total_delta theorem EXP3 BanditRLProof.Exp3RealizedHighProbabilityRegret Compiled BanditRLProof/Exp3RealizedHighProbabilityRegret.lean:147
BanditRLProof.Exp3.selectedLossCenteredSecondMoment definition EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:19
BanditRLProof.Exp3.measurable_selectedLossCenteredSecondMoment theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:27
BanditRLProof.Exp3.selectedLossCenteredSecondMoment_nonneg theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:49
BanditRLProof.Exp3.selectedLossCenteredSecondMoment_le_one theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:60
BanditRLProof.Exp3.selectedLossCenteredSecondMoment_le_lossMass theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:106
BanditRLProof.Exp3.finiteActionSelectedLossDeviation_hasMGFUpperBoundAt_variance theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:174
BanditRLProof.Exp3.finiteActionSelectedLossDeviation_compensated_hasMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:273
BanditRLProof.Exp3.sampledTrajectoryPredictableRealizedVarianceAt definition EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:298
BanditRLProof.Exp3.measurable_sampledTrajectoryPredictableRealizedVarianceAt theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:308
BanditRLProof.Exp3.sampledTrajectoryPredictableRealizedVarianceAt_nonneg theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:328
BanditRLProof.Exp3.sampledTrajectoryPredictableRealizedVarianceAt_le_lossMassAt theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:346
BanditRLProof.Exp3.sampledTrajectoryPredictableRealizedVarianceAt_le_one theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:375
BanditRLProof.Exp3.selectedLossDeviation_compensated_hasCondMGFUpperBoundAt_of_condDistrib theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:404
BanditRLProof.Exp3.sampledPredictableSelectedLossCompensated_zero_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:691
BanditRLProof.Exp3.sampledPredictableSelectedLossCompensated_succ_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:753
BanditRLProof.Exp3.sampledPredictableRealizedCompensated_zero_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:822
BanditRLProof.Exp3.sampledPredictableRealizedCompensated_succ_hasCondMGFUpperBoundAt theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:903
BanditRLProof.Exp3.sampledPredictableRealizedVarianceProcess definition EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:990
BanditRLProof.Exp3.measurable_sampledTrajectoryPredictableRealizedVarianceAt_filtration theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:1001
BanditRLProof.Exp3.sampledPredictableRealizedVarianceProcess_isPredictable theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:1062
BanditRLProof.Exp3.sampledPredictableRealizedVarianceProcess_sum_range_succ theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:1082
BanditRLProof.Exp3.sampledPredictableRealizedVariance_sum_le_lossMass theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:1102
BanditRLProof.Exp3.sampledPredictableRealizedVariance_sum_le_horizon theorem EXP3 BanditRLProof.Exp3RealizedPredictableVariance Compiled BanditRLProof/Exp3RealizedPredictableVariance.lean:1123
BanditRLProof.Exp3.sampledRealizedPredictableVarianceGeometricRadius definition EXP3 BanditRLProof.Exp3RealizedPredictableVarianceAllTime Compiled BanditRLProof/Exp3RealizedPredictableVarianceAllTime.lean:26
BanditRLProof.Exp3.sampledPredictableRealizedDeviationAllTimeFailureSet definition EXP3 BanditRLProof.Exp3RealizedPredictableVarianceAllTime Compiled BanditRLProof/Exp3RealizedPredictableVarianceAllTime.lean:33
BanditRLProof.Exp3.mem_sampledPredictableRealizedDeviationAllTimeFailureSet_iff theorem EXP3 BanditRLProof.Exp3RealizedPredictableVarianceAllTime Compiled BanditRLProof/Exp3RealizedPredictableVarianceAllTime.lean:51
BanditRLProof.Exp3.measure_sampledPredictableRealizedDeviationAllTimeFailureSet_le theorem EXP3 BanditRLProof.Exp3RealizedPredictableVarianceAllTime Compiled BanditRLProof/Exp3RealizedPredictableVarianceAllTime.lean:74
BanditRLProof.Exp3.sampledRealizedPredictableVarianceMaximalRadius definition EXP3 BanditRLProof.Exp3RealizedPredictableVarianceMaximal Compiled BanditRLProof/Exp3RealizedPredictableVarianceMaximal.lean:19
BanditRLProof.Exp3.sampledPredictableRealizedDeviation_prefix_max_tail_predictableVariance_delta theorem EXP3 BanditRLProof.Exp3RealizedPredictableVarianceMaximal Compiled BanditRLProof/Exp3RealizedPredictableVarianceMaximal.lean:26
BanditRLProof.Exp3.sampledPredictableRealizedCompensatedProcess definition EXP3 BanditRLProof.Exp3RealizedPredictableVarianceTail Compiled BanditRLProof/Exp3RealizedPredictableVarianceTail.lean:19
BanditRLProof.Exp3.sampledPredictableRealizedCompensatedProcess_stronglyAdapted theorem EXP3 BanditRLProof.Exp3RealizedPredictableVarianceTail Compiled BanditRLProof/Exp3RealizedPredictableVarianceTail.lean:31
BanditRLProof.Exp3.sampledPredictableRealizedCompensatedProcess_sum_range_succ theorem EXP3 BanditRLProof.Exp3RealizedPredictableVarianceTail Compiled BanditRLProof/Exp3RealizedPredictableVarianceTail.lean:53
BanditRLProof.Exp3.sampledPredictableRealizedDeviation_sum_tail_predictableVariance_fixedTilt theorem EXP3 BanditRLProof.Exp3RealizedPredictableVarianceTail Compiled BanditRLProof/Exp3RealizedPredictableVarianceTail.lean:75
BanditRLProof.Exp3.sampledRealizedPredictableVarianceRadius definition EXP3 BanditRLProof.Exp3RealizedPredictableVarianceTail Compiled BanditRLProof/Exp3RealizedPredictableVarianceTail.lean:168
BanditRLProof.Exp3.sampledPredictableRealizedDeviation_sum_tail_predictableVariance_delta theorem EXP3 BanditRLProof.Exp3RealizedPredictableVarianceTail Compiled BanditRLProof/Exp3RealizedPredictableVarianceTail.lean:173
BanditRLProof.Exp3.sampledTrajectoryRealizedLossAt definition EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:20
BanditRLProof.Exp3.sampledTrajectoryRealizedLossAt_ae_eq_selectedPredictable theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:27
BanditRLProof.Exp3.measurable_sampledTrajectorySelectedPredictableLossAt theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:58
BanditRLProof.Exp3.sampledTrajectorySelectedPredictableLossAt_mem_unitInterval theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:80
BanditRLProof.Exp3.integrable_sampledTrajectorySelectedPredictableLossAt theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:93
BanditRLProof.Exp3.integrable_sampledTrajectoryRealizedLossAt theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:108
BanditRLProof.Exp3.sampledPredictableRealizedInitial_integral_eq_explored theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:130
BanditRLProof.Exp3.sampledPredictableRealizedSuccessor_integral_eq_explored theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:217
BanditRLProof.Exp3.sampledPredictableRealizedAt_integral_eq_explored theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:320
BanditRLProof.Exp3.sampledPredictableRealized_finiteHorizon_integral_eq_explored theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:346
BanditRLProof.Exp3.sampledPredictable_realizedExpectedRegret_le theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:396
BanditRLProof.Exp3.sampledPredictable_realizedExpectedRegret_le_four_mul_sqrt theorem EXP3 BanditRLProof.Exp3RealizedRegret Compiled BanditRLProof/Exp3RealizedRegret.lean:457
BanditRLProof.Exp3.sampledTrajectoryRealizedRegret_eq_predictableRegret_add_realizedDeviation theorem EXP3 BanditRLProof.Exp3RealizedRegretAllTime Compiled BanditRLProof/Exp3RealizedRegretAllTime.lean:23
BanditRLProof.Exp3.sampledRealizedRegretGeometricAllTimeBudget definition EXP3 BanditRLProof.Exp3RealizedRegretAllTime Compiled BanditRLProof/Exp3RealizedRegretAllTime.lean:47
BanditRLProof.Exp3.sampledRealizedRegretGeometricAllTimeFailureSet definition EXP3 BanditRLProof.Exp3RealizedRegretAllTime Compiled BanditRLProof/Exp3RealizedRegretAllTime.lean:56
BanditRLProof.Exp3.mem_sampledRealizedRegretGeometricAllTimeFailureSet_iff theorem EXP3 BanditRLProof.Exp3RealizedRegretAllTime Compiled BanditRLProof/Exp3RealizedRegretAllTime.lean:72
BanditRLProof.Exp3.sampledRealizedRegretGeometricAllTimeFailureSet_subset theorem EXP3 BanditRLProof.Exp3RealizedRegretAllTime Compiled BanditRLProof/Exp3RealizedRegretAllTime.lean:91
BanditRLProof.Exp3.measure_sampledRealizedRegretGeometricAllTimeFailureSet_le theorem EXP3 BanditRLProof.Exp3RealizedRegretAllTime Compiled BanditRLProof/Exp3RealizedRegretAllTime.lean:145
BanditRLProof.Exp3.historyWeight definition EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:26
BanditRLProof.Exp3.historyTotalWeight definition EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:32
BanditRLProof.Exp3.normalizedHistoryDistribution definition EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:38
BanditRLProof.Exp3.exploredHistoryDistribution definition EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:46
BanditRLProof.Exp3.historyTotalWeight_pos theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:53
BanditRLProof.Exp3.normalizedHistoryDistribution_nonneg theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:63
BanditRLProof.Exp3.sum_normalizedHistoryDistribution theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:72
BanditRLProof.Exp3.exploredHistoryDistribution_nonneg theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:87
BanditRLProof.Exp3.sum_exploredHistoryDistribution theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:100
BanditRLProof.Exp3.exploredHistoryDistribution_floor theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:115
BanditRLProof.Exp3.explorationFloor_pos theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:128
BanditRLProof.Exp3.finiteActionDistribution_exploredHistoryDistribution theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:135
BanditRLProof.Exp3.measurable_historyWeight theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:148
BanditRLProof.Exp3.measurable_historyTotalWeight theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:155
BanditRLProof.Exp3.measurable_normalizedHistoryDistribution theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:166
BanditRLProof.Exp3.measurable_exploredHistoryDistribution theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:178
BanditRLProof.Exp3.MeasurableFiniteHistoryScore structure EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:192
BanditRLProof.Exp3.normalizedHistoryDistributionSource definition EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:203
BanditRLProof.Exp3.exploredHistoryDistributionSource definition EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:226
BanditRLProof.Exp3.initialExploredDistribution definition EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:247
BanditRLProof.Exp3.finiteActionDistribution_initialExploredDistribution theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:252
BanditRLProof.Exp3.exploredHistoryAlgorithm definition EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:263
BanditRLProof.Exp3.exploredHistoryAlgorithm_policy theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:290
BanditRLProof.Exp3.exploredTrajectoryKernel definition EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:310
BanditRLProof.Exp3.exploredTrajectoryMeasure_condDistrib_action theorem EXP3 BanditRLProof.Exp3RecursiveTrajectory Compiled BanditRLProof/Exp3RecursiveTrajectory.lean:349
BanditRLProof.Exp3.sampledTrajectoryObservedLoss definition EXP3 BanditRLProof.Exp3SampledHedge Compiled BanditRLProof/Exp3SampledHedge.lean:23
BanditRLProof.Exp3.previousPairHistory_frestrictLe theorem EXP3 BanditRLProof.Exp3SampledHedge Compiled BanditRLProof/Exp3SampledHedge.lean:32
BanditRLProof.Exp3.sampledHistoryScore_frestrictLe_eq_cumulativeLoss theorem EXP3 BanditRLProof.Exp3SampledHedge Compiled BanditRLProof/Exp3SampledHedge.lean:41
BanditRLProof.Exp3.distribution_sampledTrajectoryObservedLoss_succ theorem EXP3 BanditRLProof.Exp3SampledHedge Compiled BanditRLProof/Exp3SampledHedge.lean:66
BanditRLProof.Exp3.sampledTrajectoryProbabilityAt_eq_mix_distribution theorem EXP3 BanditRLProof.Exp3SampledHedge Compiled BanditRLProof/Exp3SampledHedge.lean:86
BanditRLProof.Exp3.sampledTrajectoryProbabilityAt_nonneg theorem EXP3 BanditRLProof.Exp3SampledHedge Compiled BanditRLProof/Exp3SampledHedge.lean:103
BanditRLProof.Exp3.sampledTrajectoryObservedLoss_nonneg theorem EXP3 BanditRLProof.Exp3SampledHedge Compiled BanditRLProof/Exp3SampledHedge.lean:121
BanditRLProof.Exp3.sampledTrajectory_hedge_regret_le theorem EXP3 BanditRLProof.Exp3SampledHedge Compiled BanditRLProof/Exp3SampledHedge.lean:135
BanditRLProof.Exp3.sampledHistoryScore_hedge_regret_le theorem EXP3 BanditRLProof.Exp3SampledHedge Compiled BanditRLProof/Exp3SampledHedge.lean:162
BanditRLProof.Exp3.previousPairHistory definition EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:25
BanditRLProof.Exp3.measurable_previousPairHistory theorem EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:32
BanditRLProof.Exp3.measurable_observedImportanceWeightedLoss theorem EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:47
BanditRLProof.Exp3.sampledHistoryScore definition EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:71
BanditRLProof.Exp3.sampledHistoryScore_zero theorem EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:91
BanditRLProof.Exp3.sampledHistoryScore_succ theorem EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:104
BanditRLProof.Exp3.measurable_sampledHistoryScore theorem EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:121
BanditRLProof.Exp3.measurableFiniteHistoryScore_sampledHistoryScore theorem EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:199
BanditRLProof.Exp3.sampledHistoryDistribution definition EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:210
BanditRLProof.Exp3.sampledHistoryDistribution_floor theorem EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:217
BanditRLProof.Exp3.sampledImportanceWeightedHistoryAlgorithm definition EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:229
BanditRLProof.Exp3.sampledImportanceWeightedHistoryAlgorithm_policy theorem EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:243
BanditRLProof.Exp3.sampledImportanceWeightedTrajectoryKernel definition EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:262
BanditRLProof.Exp3.sampledImportanceWeightedTrajectoryMeasure_condDistrib_action theorem EXP3 BanditRLProof.Exp3SampledHistoryScore Compiled BanditRLProof/Exp3SampledHistoryScore.lean:297
BanditRLProof.Exp3.BoundedMeasurableLossWithProbabilityFloor structure EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:20
BanditRLProof.Exp3.BoundedMeasurableLossWithProbabilityFloor.prob_pos theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:33
BanditRLProof.Exp3.measurable_importanceWeightedLoss_score theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:46
BanditRLProof.Exp3.measurable_mixedImportanceWeightedLoss_score theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:68
BanditRLProof.Exp3.measurable_weightedImportanceWeightedLoss_score theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:87
BanditRLProof.Exp3.measurable_mixedSquaredImportanceWeightedLoss_score theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:107
BanditRLProof.Exp3.norm_importanceWeightedLoss_score_le_inv_floor theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:126
BanditRLProof.Exp3.norm_mixedImportanceWeightedLoss_score_le_inv_floor theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:148
BanditRLProof.Exp3.norm_weightedImportanceWeightedLoss_score_le_inv_floor theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:186
BanditRLProof.Exp3.norm_mixedSquaredImportanceWeightedLoss_score_le_inv_floor_sq theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:224
BanditRLProof.Exp3.integrable_importanceWeightedLoss_score theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:268
BanditRLProof.Exp3.integrable_mixedImportanceWeightedLoss_score theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:292
BanditRLProof.Exp3.integrable_weightedImportanceWeightedLoss_score theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:316
BanditRLProof.Exp3.integrable_mixedSquaredImportanceWeightedLoss_score theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:340
BanditRLProof.Exp3.integrable_importanceWeightedLoss_selected_of_isFiniteMeasure theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:364
BanditRLProof.Exp3.integrable_weightedImportanceWeightedLoss_selected_of_isFiniteMeasure theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:391
BanditRLProof.Exp3.integrable_mixedSquaredImportanceWeightedLoss_selected_of_isFiniteMeasure theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:418
BanditRLProof.Exp3.actionProcess_integral_importanceWeightedLoss_eq_integral_loss_of_regularity theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:443
BanditRLProof.Exp3.actionProcess_integral_mixedImportanceWeightedLoss_eq_integral_mixedLoss_of_regularity theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:470
BanditRLProof.Exp3.actionProcess_integral_mixedSquaredImportanceWeightedLoss_eq_integral_sum_loss_sq_of_regularity theorem EXP3 BanditRLProof.Exp3ScoreRegularity Compiled BanditRLProof/Exp3ScoreRegularity.lean:496
BanditRLProof.Exp3.sampledPredictable_exploredExpectedRegret_le_horizon theorem EXP3 BanditRLProof.Exp3UniformRegret Compiled BanditRLProof/Exp3UniformRegret.lean:20
BanditRLProof.Exp3.sampledPredictable_realizedExpectedRegret_le_horizon theorem EXP3 BanditRLProof.Exp3UniformRegret Compiled BanditRLProof/Exp3UniformRegret.lean:93
BanditRLProof.Exp3.clippedExplorationRate definition EXP3 BanditRLProof.Exp3UniformRegret Compiled BanditRLProof/Exp3UniformRegret.lean:150
BanditRLProof.Exp3.clippedLearningRate definition EXP3 BanditRLProof.Exp3UniformRegret Compiled BanditRLProof/Exp3UniformRegret.lean:154
BanditRLProof.Exp3.clippedExplorationRate_nonneg theorem EXP3 BanditRLProof.Exp3UniformRegret Compiled BanditRLProof/Exp3UniformRegret.lean:157
BanditRLProof.Exp3.clippedExplorationRate_le_half theorem EXP3 BanditRLProof.Exp3UniformRegret Compiled BanditRLProof/Exp3UniformRegret.lean:162
BanditRLProof.Exp3.clippedExplorationRate_eq_tuned theorem EXP3 BanditRLProof.Exp3UniformRegret Compiled BanditRLProof/Exp3UniformRegret.lean:166
BanditRLProof.Exp3.clippedPredictableTrajectoryKernel definition EXP3 BanditRLProof.Exp3UniformRegret Compiled BanditRLProof/Exp3UniformRegret.lean:172
BanditRLProof.Exp3.sampledPredictable_clippedRealizedExpectedRegret_le_min theorem EXP3 BanditRLProof.Exp3UniformRegret Compiled BanditRLProof/Exp3UniformRegret.lean:190
BanditRLProof.ExpectationBochnerSums.integral_finset_sum theorem Foundations BanditRLProof.ExpectationBochnerSums Compiled BanditRLProof/ExpectationBochnerSums.lean:27
BanditRLProof.ExpectationBochnerSums.integral_univ_sum theorem Foundations BanditRLProof.ExpectationBochnerSums Compiled BanditRLProof/ExpectationBochnerSums.lean:51
BanditRLProof.lintegral_univ_sum_gap_mul_natCast_pullCount_le_sum_gap_mul_time theorem Foundations BanditRLProof.ExpectationFiniteBanditBounds Compiled BanditRLProof/ExpectationFiniteBanditBounds.lean:26
BanditRLProof.lintegral_univ_sum_model_gap_ofReal_mul_natCast_pullCount_le_sum_model_gap_ofReal_mul_time theorem Foundations BanditRLProof.ExpectationFiniteBanditModelBounds Compiled BanditRLProof/ExpectationFiniteBanditModelBounds.lean:30
BanditRLProof.lintegral_actionTrace_eval_eq_indicator_one theorem Foundations BanditRLProof.ExpectationFoundation Compiled BanditRLProof/ExpectationFoundation.lean:28
BanditRLProof.lintegral_ofReal_pseudoRegret_le_sum_model_gap_ofReal_mul_time_of_nonneg theorem Foundations BanditRLProof.ExpectationPseudoRegretOfRealBounds Compiled BanditRLProof/ExpectationPseudoRegretOfRealBounds.lean:30
BanditRLProof.lintegral_ofReal_pseudoRegret_le_sum_model_gap_ofReal_mul_time_of_rat_gap_nonneg theorem Foundations BanditRLProof.ExpectationPseudoRegretRatBounds Compiled BanditRLProof/ExpectationPseudoRegretRatBounds.lean:27
BanditRLProof.lintegral_ofReal_pseudoRegret_le_sum_model_gap_ofReal_mul_time theorem Foundations BanditRLProof.ExpectationPseudoRegretRatBounds Compiled BanditRLProof/ExpectationPseudoRegretRatBounds.lean:69
BanditRLProof.ennreal_natCast_pullCount_eq_finset_range_indicator_one theorem Foundations BanditRLProof.ExpectationPullCount Compiled BanditRLProof/ExpectationPullCount.lean:21
BanditRLProof.lintegral_natCast_pullCount_eq_sum_measure_actionTrace_eval_eq theorem Foundations BanditRLProof.ExpectationPullCount Compiled BanditRLProof/ExpectationPullCount.lean:46
BanditRLProof.lintegral_natCast_pullCount_le_time theorem Foundations BanditRLProof.ExpectationPullCountBounds Compiled BanditRLProof/ExpectationPullCountBounds.lean:28
BanditRLProof.real_pseudoRegret_eq_univ_sum_gap_mul_natCast_pullCount theorem Foundations BanditRLProof.ExpectationRegretPullCount Compiled BanditRLProof/ExpectationRegretPullCount.lean:21
BanditRLProof.integrable_real_pullCount_of_measurable_action theorem Foundations BanditRLProof.ExpectationRegretPullCount Compiled BanditRLProof/ExpectationRegretPullCount.lean:41
BanditRLProof.integrable_real_pseudoRegret_of_integrable_pullCount theorem Foundations BanditRLProof.ExpectationRegretPullCount Compiled BanditRLProof/ExpectationRegretPullCount.lean:71
BanditRLProof.integral_real_pseudoRegret_eq_sum_gap_mul_integral_pullCount theorem Foundations BanditRLProof.ExpectationRegretPullCount Compiled BanditRLProof/ExpectationRegretPullCount.lean:124
BanditRLProof.lintegral_finset_sum_actionTrace_eval_eq_indicator_one theorem Foundations BanditRLProof.ExpectationSums Compiled BanditRLProof/ExpectationSums.lean:26
BanditRLProof.lintegral_finset_sum_gap_mul_natCast_pullCount_eq theorem Foundations BanditRLProof.ExpectationWeightedPullCount Compiled BanditRLProof/ExpectationWeightedPullCount.lean:30
BanditRLProof.lintegral_finset_sum_gap_mul_natCast_pullCount_le_sum_gap_mul_time theorem Foundations BanditRLProof.ExpectationWeightedPullCountBounds Compiled BanditRLProof/ExpectationWeightedPullCountBounds.lean:29
BanditRLProof.FTRL.linearLoss definition Tsallis-FTRL BanditRLProof.FTRLOneStep Compiled BanditRLProof/FTRLOneStep.lean:25
BanditRLProof.FTRL.finiteSimplex definition Tsallis-FTRL BanditRLProof.FTRLOneStep Compiled BanditRLProof/FTRLOneStep.lean:30
BanditRLProof.FTRL.regularizedObjective definition Tsallis-FTRL BanditRLProof.FTRLOneStep Compiled BanditRLProof/FTRLOneStep.lean:40
BanditRLProof.FTRL.IsRegularizedMinimizer definition Tsallis-FTRL BanditRLProof.FTRLOneStep Compiled BanditRLProof/FTRLOneStep.lean:47
BanditRLProof.FTRL.linearLoss_sub_le_regularizer_sub_div_of_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.FTRLOneStep Compiled BanditRLProof/FTRLOneStep.lean:63
BanditRLProof.FTRL.linearLoss_sub_le_regularizer_sub_div_of_simplex_minimizer theorem Tsallis-FTRL BanditRLProof.FTRLOneStep Compiled BanditRLProof/FTRLOneStep.lean:94
BanditRLProof.Concentration.finiteArmIntervalVarianceProxy definition Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:18
BanditRLProof.Concentration.intervalVarianceProxy_le_finiteArmIntervalVarianceProxy theorem Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:23
BanditRLProof.Concentration.finiteArmIntervalVarianceProxy_pos theorem Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:36
BanditRLProof.Concentration.finiteArmVarianceProxy definition Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:55
BanditRLProof.Concentration.varianceProxy_le_finiteArmVarianceProxy theorem Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:60
BanditRLProof.Concentration.finiteArmVarianceProxy_pos_of_exists theorem Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:71
BanditRLProof.Concentration.finiteArmPositiveVarianceProxy definition Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:84
BanditRLProof.Concentration.varianceProxy_le_finiteArmPositiveVarianceProxy theorem Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:89
BanditRLProof.Concentration.finiteArmPositiveVarianceProxy_pos theorem Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:97
BanditRLProof.RewardKernel.contextIndependentCenteredRewardKernelLaw_of_hasSubgaussianMGF definition Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:112
BanditRLProof.RewardKernel.contextIndependentBoundedCenteredRewardKernelLaw definition Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:162
BanditRLProof.RewardKernel.contextIndependentArmwiseBoundedCenteredRewardKernelLaw definition Probability layer BanditRLProof.FiniteArmRewardKernelLaw Compiled BanditRLProof/FiniteArmRewardKernelLaw.lean:203
BanditRLProof.FiniteBanditModel.mean_le_foldl_select theorem Foundations BanditRLProof.FiniteBanditModelInvariants Compiled BanditRLProof/FiniteBanditModelInvariants.lean:18
BanditRLProof.FiniteBanditModel.mean_le_bestArm_mean theorem Foundations BanditRLProof.FiniteBanditModelInvariants Compiled BanditRLProof/FiniteBanditModelInvariants.lean:66
BanditRLProof.FiniteBanditModel.gap_nonneg theorem Foundations BanditRLProof.FiniteBanditModelInvariants Compiled BanditRLProof/FiniteBanditModelInvariants.lean:84
BanditRLProof.FiniteBanditModel.maxGap definition Foundations BanditRLProof.FiniteBanditModelInvariants Compiled BanditRLProof/FiniteBanditModelInvariants.lean:99
BanditRLProof.FiniteBanditModel.gap_le_maxGap theorem Foundations BanditRLProof.FiniteBanditModelInvariants Compiled BanditRLProof/FiniteBanditModelInvariants.lean:114
BanditRLProof.FiniteBanditModel.maxGap_nonneg theorem Foundations BanditRLProof.FiniteBanditModelInvariants Compiled BanditRLProof/FiniteBanditModelInvariants.lean:123
BanditRLProof.Concentration.finiteContextArmVarianceProxy definition Probability layer BanditRLProof.FiniteContextVarianceProxy Compiled BanditRLProof/FiniteContextVarianceProxy.lean:14
BanditRLProof.Concentration.varianceProxy_le_finiteContextArmVarianceProxy theorem Probability layer BanditRLProof.FiniteContextVarianceProxy Compiled BanditRLProof/FiniteContextVarianceProxy.lean:20
BanditRLProof.Concentration.finiteContextArmVarianceProxy_pos_of_exists theorem Probability layer BanditRLProof.FiniteContextVarianceProxy Compiled BanditRLProof/FiniteContextVarianceProxy.lean:37
BanditRLProof.Concentration.finiteContextArmPositiveVarianceProxy definition Probability layer BanditRLProof.FiniteContextVarianceProxy Compiled BanditRLProof/FiniteContextVarianceProxy.lean:53
BanditRLProof.Concentration.varianceProxy_le_finiteContextArmPositiveVarianceProxy theorem Probability layer BanditRLProof.FiniteContextVarianceProxy Compiled BanditRLProof/FiniteContextVarianceProxy.lean:59
BanditRLProof.Concentration.finiteContextArmPositiveVarianceProxy_pos theorem Probability layer BanditRLProof.FiniteContextVarianceProxy Compiled BanditRLProof/FiniteContextVarianceProxy.lean:70
BanditRLProof.FiniteRealArgmax.score_le_foldl_select theorem Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:21
BanditRLProof.FiniteRealArgmax.chooseFin definition Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:63
BanditRLProof.FiniteRealArgmax.score_le_chooseFin theorem Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:70
BanditRLProof.FiniteRealArgmax.measurable_selected_score theorem Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:78
BanditRLProof.FiniteRealArgmax.measurable_foldl_select theorem Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:98
BanditRLProof.FiniteRealArgmax.measurable_chooseFin_of_forall_measurable theorem Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:132
BanditRLProof.FiniteRealArgmax.choose definition Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:143
BanditRLProof.FiniteRealArgmax.score_le_choose theorem Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:151
BanditRLProof.FiniteRealArgmax.measurable_choose_of_forall_measurable theorem Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:161
BanditRLProof.FiniteRealArgmax.measurable_selected_score_of_forall_measurable theorem Foundations BanditRLProof.FiniteRealArgmax Compiled BanditRLProof/FiniteRealArgmax.lean:180
BanditRLProof.History.FiniteActionHistory abbreviation Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:22
BanditRLProof.History.FiniteRewardHistory abbreviation Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:27
BanditRLProof.History.FinitePairHistory abbreviation Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:31
BanditRLProof.History.FiniteHistory abbreviation Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:35
BanditRLProof.History.finiteActionHistoryOfTrace definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:40
BanditRLProof.History.finiteRewardHistoryOfTrace definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:48
BanditRLProof.History.completeRewardTrace definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:62
BanditRLProof.History.finiteHistoryOfTrace definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:69
BanditRLProof.History.finitePairHistoryOfTrace definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:78
BanditRLProof.History.extendPairHistorySucc definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:87
BanditRLProof.History.finiteActionHistoryOfTrace_apply theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:99
BanditRLProof.History.finiteRewardHistoryOfTrace_apply theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:105
BanditRLProof.History.completeRewardTrace_finiteRewardHistoryOfTrace_apply_of_le theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:115
BanditRLProof.History.finiteHistoryOfTrace_fst theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:124
BanditRLProof.History.finiteHistoryOfTrace_snd theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:133
BanditRLProof.History.finitePairHistoryOfTrace_apply theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:142
BanditRLProof.History.extendPairHistorySucc_apply_of_le theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:151
BanditRLProof.History.extendPairHistorySucc_apply_succ theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:161
BanditRLProof.History.finitePairHistoryOfTrace_succ theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:175
BanditRLProof.History.pairHistoryRewardProjection definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:193
BanditRLProof.History.pairHistoryRewardProjection_apply theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:200
BanditRLProof.History.pairHistoryRewardProjection_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:207
BanditRLProof.History.measurable_finiteActionHistory_eval theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:217
BanditRLProof.History.measurable_finiteRewardHistory_eval theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:224
BanditRLProof.History.measurable_finiteHistory_action_eval theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:231
BanditRLProof.History.measurable_finiteHistory_reward_eval theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:241
BanditRLProof.History.measurable_pairHistoryRewardProjection theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:251
BanditRLProof.History.measurable_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:266
BanditRLProof.History.measurable_extendPairHistorySucc theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:285
BanditRLProof.History.measurable_finiteActionHistoryOfTrace theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:310
BanditRLProof.History.measurable_finiteRewardHistoryOfTrace theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:326
BanditRLProof.History.measurable_finiteHistoryOfTrace theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:342
BanditRLProof.History.historyGenerators definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:367
BanditRLProof.History.historyGenerators_mono theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:381
BanditRLProof.History.historyMeasurableSpace definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:413
BanditRLProof.History.historyMeasurableSpace_mono theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:421
BanditRLProof.History.historyMeasurableSpace_le theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:435
BanditRLProof.History.historyFiltration definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:476
BanditRLProof.History.historyFiltration_apply theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:493
BanditRLProof.History.historyFiltrationSucc definition Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:516
BanditRLProof.History.historyFiltrationSucc_apply theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:536
BanditRLProof.History.measurableSet_action_mem_historyFiltration theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:553
BanditRLProof.History.measurable_action_mem_historyFiltration_of_lt theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:579
BanditRLProof.History.measurableSet_reward_mem_historyFiltration theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:603
BanditRLProof.History.measurable_reward_mem_historyFiltration_of_lt theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:629
BanditRLProof.History.measurable_finitePairHistoryOfTrace_mem_historyFiltration_of_lt theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:661
BanditRLProof.History.historyFiltration_succ_eq_comap_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:716
BanditRLProof.History.historyFiltrationSucc_eq_comap_finitePairHistoryOfTrace theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:819
BanditRLProof.History.historyFiltrationSucc_eq_of_action_eq_on_prefix theorem Probability layer BanditRLProof.HistoryFiltration Compiled BanditRLProof/HistoryFiltration.lean:849
BanditRLProof.IndependenceFoundation.iIndepFun_infinitePi_coord theorem Probability layer BanditRLProof.IndependenceFoundation Compiled BanditRLProof/IndependenceFoundation.lean:22
BanditRLProof.IndependenceFoundation.iIndepFun_rewardTrace_infinitePi theorem Probability layer BanditRLProof.IndependenceFoundation Compiled BanditRLProof/IndependenceFoundation.lean:44
BanditRLProof.IntegrabilitySums.integrable_finset_sum theorem Probability layer BanditRLProof.IntegrabilitySums Compiled BanditRLProof/IntegrabilitySums.lean:26
BanditRLProof.IntegrabilitySums.integrable_univ_sum theorem Probability layer BanditRLProof.IntegrabilitySums Compiled BanditRLProof/IntegrabilitySums.lean:49
BanditRLProof.IndepFun.comp_of_map theorem Probability layer BanditRLProof.KernelIndependentExtension Compiled BanditRLProof/KernelIndependentExtension.lean:19
BanditRLProof.indepFun_fst_snd_compProd_comap_of_indepFun theorem Probability layer BanditRLProof.KernelIndependentExtension Compiled BanditRLProof/KernelIndependentExtension.lean:39
BanditRLProof.KernelTrajectoryPrefix.partialTraj_zero_congr theorem Probability layer BanditRLProof.KernelTrajectoryPrefix Compiled BanditRLProof/KernelTrajectoryPrefix.lean:22
BanditRLProof.KernelTrajectoryPrefix.trajMeasure_map_frestrictLe_congr theorem Probability layer BanditRLProof.KernelTrajectoryPrefix Compiled BanditRLProof/KernelTrajectoryPrefix.lean:41
BanditRLProof.pullCount_one theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:18
BanditRLProof.pullCount_succ_of_eq theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:22
BanditRLProof.pullCount_succ_of_ne theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:26
BanditRLProof.pullCount_le_succ theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:30
BanditRLProof.pullCount_succ_le_succ theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:35
BanditRLProof.pullCount_mono theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:40
BanditRLProof.pullCount_le_time theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:46
BanditRLProof.pullCount_add_le theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:58
BanditRLProof.pullCount_le_add theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:67
BanditRLProof.pullCount_eq_zero_of_forall_ne theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:71
BanditRLProof.pullCount_eq_time_of_forall_eq theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:80
BanditRLProof.pullCount_pos_of_eq_before theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:89
BanditRLProof.pullCount_eq_of_forall_lt theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:108
BanditRLProof.pullCount_const_self theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:124
BanditRLProof.pullCount_const_of_ne theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:130
BanditRLProof.pullCount_add_eq_of_forall_ne_between theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:136
BanditRLProof.pullCount_add_eq_add_of_forall_eq_between theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:148
BanditRLProof.pullCount_eq_list_filter_length theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:168
BanditRLProof.sumRewards_succ_of_eq theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:189
BanditRLProof.sumRewards_succ_of_ne theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:194
BanditRLProof.sumRewards_eq_zero_of_forall_ne theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:200
BanditRLProof.sumRewards_const_of_ne theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:209
BanditRLProof.sumRewards_add_eq_of_forall_ne_between theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:217
BanditRLProof.sumRewards_eq_list_range_foldl theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:235
BanditRLProof.sumRewards_eq_list_range_filter_foldl theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:253
BanditRLProof.FiniteBanditModel.bestMean_eq_mean_bestArm theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:272
BanditRLProof.FiniteBanditModel.gap_of_ne_bestArm theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:275
BanditRLProof.pseudoRegret_one theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:286
BanditRLProof.pseudoRegret_succ_of_bestArm theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:291
BanditRLProof.pseudoRegret_succ_of_gap_zero theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:296
BanditRLProof.pseudoRegret_eq_zero_of_forall_bestArm theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:301
BanditRLProof.pseudoRegret_eq_zero_of_forall_gap_zero theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:310
BanditRLProof.pseudoRegret_const_bestArm theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:319
BanditRLProof.pseudoRegret_const_of_gap_zero theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:325
BanditRLProof.pseudoRegret_add_eq_of_forall_bestArm_between theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:331
BanditRLProof.pseudoRegret_add_eq_of_forall_gap_zero_between theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:343
BanditRLProof.pseudoRegret_eq_list_range_foldl theorem Foundations BanditRLProof.LeafLemmas Compiled BanditRLProof/LeafLemmas.lean:361
BanditRLProof.UpstreamRef structure Frontier BanditRLProof.Literature Compiled BanditRLProof/Literature.lean:12
BanditRLProof.lmlRef definition Frontier BanditRLProof.Literature Compiled BanditRLProof/Literature.lean:22
BanditRLProof.lmlBanditDeclarationCards definition Frontier BanditRLProof.Literature Compiled BanditRLProof/Literature.lean:31
BanditRLProof.LowerBounds.pairHistoryZeroMeasurableEquiv definition Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:24
BanditRLProof.LowerBounds.pairHistorySuccMeasurableEquiv definition Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:43
BanditRLProof.LowerBounds.pairHistoryZeroMeasurableEquiv_apply theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:56
BanditRLProof.LowerBounds.pairHistorySuccMeasurableEquiv_apply theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:67
BanditRLProof.LowerBounds.stationaryBanditHistoryEnvironment definition Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:89
BanditRLProof.LowerBounds.stationaryBanditHistoryEnvironment_initialFeedback theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:98
BanditRLProof.LowerBounds.stationaryBanditHistoryEnvironment_feedback_apply theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:105
BanditRLProof.LowerBounds.canonicalBanditHistoryMeasure definition Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:116
BanditRLProof.LowerBounds.canonicalBanditHistoryMeasure_zero theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:138
BanditRLProof.LowerBounds.canonicalBanditHistoryMeasure_succ theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:181
BanditRLProof.LowerBounds.klDiv_canonicalBanditHistoryMeasure_zero theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:240
BanditRLProof.LowerBounds.klDiv_canonicalBanditHistoryMeasure_succ theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:263
BanditRLProof.LowerBounds.canonicalPolicyArmMass definition Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:294
BanditRLProof.LowerBounds.canonicalExpectedPullCountThrough definition Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:310
BanditRLProof.LowerBounds.canonicalExpectedPullCountThrough_zero theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:321
BanditRLProof.LowerBounds.canonicalExpectedPullCountThrough_succ theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:331
BanditRLProof.LowerBounds.lintegral_lintegral_fin_eq_sum_armMass_mul theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:344
BanditRLProof.LowerBounds.klDiv_canonicalBanditHistoryMeasure_eq_sum_expectedPullCount_mul_armKL theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:367
BanditRLProof.LowerBounds.finiteHistoryPullCountENNReal definition Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:401
BanditRLProof.LowerBounds.measurable_finiteHistoryPullCountENNReal theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:410
BanditRLProof.LowerBounds.finiteHistoryPullCountENNReal_pairHistoryZeroMeasurableEquiv theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:431
BanditRLProof.LowerBounds.finiteHistoryPullCountENNReal_pairHistorySuccMeasurableEquiv theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:443
BanditRLProof.LowerBounds.canonicalRealizedExpectedPullCountThrough definition Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:457
BanditRLProof.LowerBounds.lintegral_historyStepKernel_armIndicator_eq_policy_mass theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:468
BanditRLProof.LowerBounds.canonicalRealizedExpectedPullCountThrough_zero theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:505
BanditRLProof.LowerBounds.canonicalRealizedExpectedPullCountThrough_succ theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:538
BanditRLProof.LowerBounds.canonicalRealizedExpectedPullCountThrough_eq_expectedPullCountThrough theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:597
BanditRLProof.LowerBounds.klDiv_canonicalBanditHistoryMeasure_zero_general theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:614
BanditRLProof.LowerBounds.klDiv_canonicalBanditHistoryMeasure_succ_general theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:632
BanditRLProof.LowerBounds.klDiv_canonicalBanditHistoryMeasure_eq_sum_expectedPullCount_mul_armKL_general theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:662
BanditRLProof.LowerBounds.klDiv_canonicalBanditHistoryMeasure_eq_sum_realizedExpectedPullCount_mul_armKL theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:702
BanditRLProof.LowerBounds.banditHistoryRelativeEntropy_eq_expectedPulls_sum theorem Foundations BanditRLProof.LowerBounds.BanditHistoryKL Compiled BanditRLProof/LowerBounds/BanditHistoryKL.lean:726
BanditRLProof.LowerBounds.worstCaseExpectedRegret definition Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:35
BanditRLProof.LowerBounds.minimaxExpectedRegret definition Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:49
BanditRLProof.LowerBounds.expectedRegret_le_worstCaseExpectedRegret theorem Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:58
BanditRLProof.LowerBounds.minimaxExpectedRegret_le_worstCaseExpectedRegret theorem Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:71
BanditRLProof.LowerBounds.le_minimaxExpectedRegret theorem Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:82
BanditRLProof.LowerBounds.exists_alternative_le_average theorem Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:100
BanditRLProof.LowerBounds.alternativeExpectedPullBudget_le theorem Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:126
BanditRLProof.LowerBounds.exists_leastExploredAlternative theorem Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:143
BanditRLProof.LowerBounds.baseEnvironmentRegret definition Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:156
BanditRLProof.LowerBounds.changedEnvironmentRegretLowerBound definition Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:161
BanditRLProof.LowerBounds.max_base_changed_regretLowerBound_ge_half_sub_error theorem Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:173
BanditRLProof.LowerBounds.max_base_changed_regretLowerBound_ge_half theorem Foundations BanditRLProof.LowerBounds.BasicIdeas Compiled BanditRLProof/LowerBounds/BasicIdeas.lean:205
BanditRLProof.LowerBounds.klDiv_compProd_same_left_eq_lintegral_kernelRN_ae theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:35
BanditRLProof.LowerBounds.klDiv_compProd_same_left_eq_lintegral_kernelRN theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:98
BanditRLProof.LowerBounds.klDiv_compProd_same_left_eq_lintegral_klDiv theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:120
BanditRLProof.LowerBounds.klDiv_compProd_same_left_eq_lintegral_klDiv_ae theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:155
BanditRLProof.LowerBounds.klDiv_compProd_same_left_eq_lintegral_klDiv_of_measurable theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:195
BanditRLProof.LowerBounds.klDiv_map_measurableEquiv theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:227
BanditRLProof.LowerBounds.klDiv_historyStep_samePolicy_eq_iterated_lintegral_armKL theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:290
BanditRLProof.LowerBounds.klDiv_finiteAction_compProd_eq_lintegral_armKL theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:341
BanditRLProof.LowerBounds.klDiv_finiteAction_compProd_eq_sum_mass_mul_armKL theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:356
BanditRLProof.LowerBounds.klDiv_historyStep_samePolicy_eq_iterated_lintegral_armKL_general theorem Foundations BanditRLProof.LowerBounds.ConditionalKernelKL Compiled BanditRLProof/LowerBounds/ConditionalKernelKL.lean:379
BanditRLProof.LowerBounds.tailAtLeast definition Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:31
BanditRLProof.LowerBounds.stochasticHighProbabilityThreshold definition Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:37
BanditRLProof.LowerBounds.stochasticMinimaxHighProbabilityThreshold definition Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:46
BanditRLProof.LowerBounds.adversarialHighProbabilityThreshold definition Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:56
BanditRLProof.LowerBounds.exists_tailMass_ge_of_integral_ge theorem Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:67
BanditRLProof.LowerBounds.exists_cdfTail_ge_of_integral_ge theorem Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:78
BanditRLProof.LowerBounds.measureReal_diff_ge_delta theorem Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:96
BanditRLProof.LowerBounds.adversarialRegretLowerExpression definition Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:111
BanditRLProof.LowerBounds.adversarialRegretLowerExpression_ge_quarter theorem Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:119
BanditRLProof.LowerBounds.randomRegret_ge_quarter_of_clippingDecomposition theorem Foundations BanditRLProof.LowerBounds.HighProbability Compiled BanditRLProof/LowerBounds/HighProbability.lean:133
BanditRLProof.LowerBounds.relativeEntropy abbreviation Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:26
BanditRLProof.LowerBounds.relativeEntropy_of_absolutelyContinuous_of_integrable theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:32
BanditRLProof.LowerBounds.relativeEntropy_of_probability_absolutelyContinuous_of_integrable theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:42
BanditRLProof.LowerBounds.relativeEntropy_eq_top_of_not_absolutelyContinuous theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:52
BanditRLProof.LowerBounds.relativeEntropy_ne_top_iff theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:60
BanditRLProof.LowerBounds.bernoulliRelativeEntropy abbreviation Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:67
BanditRLProof.LowerBounds.rnDeriv_restrict_restrict theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:72
BanditRLProof.LowerBounds.relativeEntropy_restrict_add_compl theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:88
BanditRLProof.LowerBounds.bernoulliKLCore_event_le theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:131
BanditRLProof.LowerBounds.mul_sqrt_div_eq_sqrt_mul theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:184
BanditRLProof.LowerBounds.exp_neg_half_bernoulliKLCore_le_affinity theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:202
BanditRLProof.LowerBounds.half_binaryAffinity_sq_le_eventError theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:270
BanditRLProof.LowerBounds.binaryBretagnolleHuberCore theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:305
BanditRLProof.LowerBounds.bretagnolleHuberScale definition Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:350
BanditRLProof.LowerBounds.bretagnolleHuberScale_nonneg theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:353
BanditRLProof.LowerBounds.binaryBretagnolleHuber theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:362
BanditRLProof.LowerBounds.bernoulliRelativeEntropy_event_le theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:395
BanditRLProof.LowerBounds.bretagnolleHuberScale_antitone theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:443
BanditRLProof.LowerBounds.bretagnolleHuber theorem Foundations BanditRLProof.LowerBounds.InformationTheory Compiled BanditRLProof/LowerBounds/InformationTheory.lean:462
BanditRLProof.LowerBounds.IsConsistentRegret definition Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:33
BanditRLProof.LowerBounds.IsConsistentPolicyOver definition Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:40
BanditRLProof.LowerBounds.IsConsistentRegret.add theorem Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:51
BanditRLProof.LowerBounds.IsConsistentRegret.eventually_add_le_rpow theorem Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:62
BanditRLProof.LowerBounds.IsConsistentRegret.eventually_log_add_div_log_le theorem Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:82
BanditRLProof.LowerBounds.divergenceInfimum definition Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:104
BanditRLProof.LowerBounds.divergenceInfimum_le theorem Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:116
BanditRLProof.LowerBounds.parametricDivergenceInfimum definition Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:130
BanditRLProof.LowerBounds.parametricDivergenceInfimum_le theorem Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:140
BanditRLProof.LowerBounds.unitGaussianDivergenceInfimum abbreviation Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:151
BanditRLProof.LowerBounds.unitGaussianDivergenceInfimum_le_perturbed theorem Foundations BanditRLProof.LowerBounds.InstanceDependent Compiled BanditRLProof/LowerBounds/InstanceDependent.lean:157
BanditRLProof.LowerBounds.unitGaussianArm abbreviation Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:27
BanditRLProof.LowerBounds.unitGaussianBandit abbreviation Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:31
BanditRLProof.LowerBounds.log_gaussianPDFReal_div_gaussianPDFReal_one theorem Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:36
BanditRLProof.LowerBounds.llr_gaussianReal_one_ae theorem Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:53
BanditRLProof.LowerBounds.integrable_llr_gaussianReal_one theorem Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:73
BanditRLProof.LowerBounds.klDiv_gaussianReal_one theorem Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:89
BanditRLProof.LowerBounds.klDiv_unitGaussianArm_zero_two_mul theorem Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:121
BanditRLProof.LowerBounds.gaussianMinimaxGap definition Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:131
BanditRLProof.LowerBounds.gaussianMinimaxGap_sq theorem Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:136
BanditRLProof.LowerBounds.gaussianMinimaxGap_informationExponent_eq_half theorem Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:147
BanditRLProof.LowerBounds.gaussianMinimaxGap_le_half theorem Foundations BanditRLProof.LowerBounds.Minimax Compiled BanditRLProof/LowerBounds/Minimax.lean:159
BanditRLProof.MartingaleDiff.SuccMartingaleDifference structure Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:24
BanditRLProof.MartingaleDiff.SuccMartingaleDifferencePrefix structure Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:46
BanditRLProof.MartingaleDiff.SuccMartingaleDifference.toPrefix theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:62
BanditRLProof.MartingaleDiff.SuccMartingaleDifference.stronglyAdapted' theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:74
BanditRLProof.MartingaleDiff.SuccMartingaleDifference.integrable' theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:83
BanditRLProof.MartingaleDiff.SuccMartingaleDifference.condExp_succ_ae_eq_zero theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:93
BanditRLProof.MartingaleDiff.SuccMartingaleDifferencePrefix.stronglyAdapted' theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:109
BanditRLProof.MartingaleDiff.SuccMartingaleDifferencePrefix.integrable_of_lt theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:119
BanditRLProof.MartingaleDiff.SuccMartingaleDifferencePrefix.condExp_succ_ae_eq_zero theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:130
BanditRLProof.MartingaleDiff.centeredRewardProcess definition Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:153
BanditRLProof.MartingaleDiff.succMartingaleDifference_centeredRewardProcess_of_condExp theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:164
BanditRLProof.MartingaleDiff.succMartingaleDifferencePrefix_centeredRewardProcess_of_condExp theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:189
BanditRLProof.MartingaleDiff.partialSumsSucc definition Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:219
BanditRLProof.MartingaleDiff.martingale_partialSumsSucc_of_succMartingaleDifference theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:234
BanditRLProof.MartingaleDiff.martingale_partialSumsSucc_centeredRewardProcess_of_condExp theorem Probability layer BanditRLProof.MartingaleDifference Compiled BanditRLProof/MartingaleDifference.lean:270
BanditRLProof.pullCount_eq_finset_filter_card theorem Foundations BanditRLProof.MathlibWrappers Compiled BanditRLProof/MathlibWrappers.lean:28
BanditRLProof.sumRewards_eq_finset_filter_sum theorem Foundations BanditRLProof.MathlibWrappers Compiled BanditRLProof/MathlibWrappers.lean:62
BanditRLProof.pseudoRegret_eq_finset_sum theorem Foundations BanditRLProof.MathlibWrappers Compiled BanditRLProof/MathlibWrappers.lean:93
BanditRLProof.sumRewards_eq_finset_range_indicator_reward theorem Probability layer BanditRLProof.MeasurableLocalQuantities Compiled BanditRLProof/MeasurableLocalQuantities.lean:16
BanditRLProof.measurable_sumRewards theorem Probability layer BanditRLProof.MeasurableLocalQuantities Compiled BanditRLProof/MeasurableLocalQuantities.lean:60
BanditRLProof.measurable_pullCount theorem Probability layer BanditRLProof.MeasurablePullCount Compiled BanditRLProof/MeasurablePullCount.lean:23
BanditRLProof.measurable_natCast_pullCount theorem Probability layer BanditRLProof.MeasurablePullCountCast Compiled BanditRLProof/MeasurablePullCountCast.lean:23
BanditRLProof.measurable_pseudoRegret theorem Probability layer BanditRLProof.MeasurableRegret Compiled BanditRLProof/MeasurableRegret.lean:24
BanditRLProof.measurable_finset_sum_indicator_reward theorem Probability layer BanditRLProof.MeasurableSums Compiled BanditRLProof/MeasurableSums.lean:24
BanditRLProof.measurableSet_actionTrace_eval_eq theorem Probability layer BanditRLProof.MeasureFoundation Compiled BanditRLProof/MeasureFoundation.lean:25
BanditRLProof.measurable_actionTrace_eval_eq_indicator_const theorem Probability layer BanditRLProof.MeasureFoundation Compiled BanditRLProof/MeasureFoundation.lean:43
BanditRLProof.measurable_actionTrace_eval_eq_indicator_reward theorem Probability layer BanditRLProof.MeasureFoundation Compiled BanditRLProof/MeasureFoundation.lean:64
BanditRLProof.integral_indicator_le_sqrt_secondMoment_mul_sqrt_real_measure theorem Probability layer BanditRLProof.MeasureL2Indicator Compiled BanditRLProof/MeasureL2Indicator.lean:21
BanditRLProof.OFUL.allTimeScheduledScalarRidgeConfidenceFailureSet definition OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:28
BanditRLProof.OFUL.mem_allTimeScheduledScalarRidgeConfidenceFailureSet_iff theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:42
BanditRLProof.OFUL.not_mem_allTimeScheduledScalarRidgeConfidenceFailureSet_iff theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:63
BanditRLProof.OFUL.measure_allTimeScheduledScalarRidgeConfidenceFailureSet_le_tsum theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:92
BanditRLProof.OFUL.allTimeTelescopingWeight definition OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:149
BanditRLProof.OFUL.allTimeTelescopingWeight_eq_sub theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:153
BanditRLProof.OFUL.sum_range_allTimeTelescopingWeight theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:162
BanditRLProof.OFUL.allTimeTelescopingWeight_nonneg theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:171
BanditRLProof.OFUL.allTimeTelescopingWeight_le_one theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:177
BanditRLProof.OFUL.hasSum_allTimeTelescopingWeight theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:197
BanditRLProof.OFUL.allTimeTelescopingDelta definition OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:215
BanditRLProof.OFUL.allTimeTelescopingDelta_eq_div theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:220
BanditRLProof.OFUL.allTimeTelescopingDelta_pos theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:227
BanditRLProof.OFUL.allTimeTelescopingDelta_le_one theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:235
BanditRLProof.OFUL.tsum_ofReal_allTimeTelescopingDelta theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:248
BanditRLProof.OFUL.allTimeTelescopingScalarRidgeConfidenceFailureSet definition OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:278
BanditRLProof.OFUL.measure_allTimeTelescopingScalarRidgeConfidenceFailureSet_le theorem OFUL BanditRLProof.OFULAllTimeConfidence Compiled BanditRLProof/OFULAllTimeConfidence.lean:296
BanditRLProof.OFUL.measurable_matrix_det_of_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:21
BanditRLProof.OFUL.measurable_matrix_adjugate_apply_of_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:35
BanditRLProof.OFUL.measurable_matrix_nonsingInv_apply_of_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:57
BanditRLProof.OFUL.measurable_matrix_mulVec_apply_of_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:73
BanditRLProof.OFUL.measurable_dotProduct_of_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:85
BanditRLProof.OFUL.measurable_confidenceWidth_of_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:95
BanditRLProof.OFUL.measurable_optimisticScore_of_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:114
BanditRLProof.OFUL.measurable_finiteHorizonFeatureGram_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:134
BanditRLProof.OFUL.measurable_finiteHorizonResponseVector_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:147
BanditRLProof.OFUL.measurable_finiteHorizonRidgeEstimate_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:163
BanditRLProof.OFUL.measurable_finiteHorizonScalarConfidenceRadius theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:188
BanditRLProof.OFUL.finiteHistoryObservedFeature definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:217
BanditRLProof.OFUL.finiteHistoryObservedResponse definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:228
BanditRLProof.OFUL.measurable_finiteHistoryObservedFeature_apply theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:238
BanditRLProof.OFUL.measurable_finiteHistoryObservedResponse theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:255
BanditRLProof.OFUL.finiteHistoryScalarRidgeEstimate definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:268
BanditRLProof.OFUL.finiteHistoryScalarRidgeDesign definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:284
BanditRLProof.OFUL.finiteHistoryScalarRidgeRadius definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:298
BanditRLProof.OFUL.finiteHistoryFixedActionFeature definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:311
BanditRLProof.OFUL.finiteHistoryScalarRidgeOptimisticScore definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:319
BanditRLProof.OFUL.measurable_finiteHistoryScalarRidgeOptimisticScore theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:338
BanditRLProof.OFUL.finiteHistoryScalarRidgeOptimisticAction definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:386
BanditRLProof.OFUL.finiteHistoryScalarRidgeOptimisticAction_score_max theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:404
BanditRLProof.OFUL.finiteHistoryScalarRidgeOptimisticAlgorithm definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:431
BanditRLProof.OFUL.finiteHistoryScalarRidgeSelectedFeature definition OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:449
BanditRLProof.OFUL.canonicalHistoryTrajectory_observedFeature_succ_ae_eq_finiteHistoryScalarRidgeSelectedFeature theorem OFUL BanditRLProof.OFULConcreteHistoryRidgeSelection Compiled BanditRLProof/OFULConcreteHistoryRidgeSelection.lean:466
BanditRLProof.OFUL.matrixNorm definition OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:20
BanditRLProof.OFUL.matrixNorm_add_le theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:26
BanditRLProof.OFUL.matrixNorm_sub_le theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:43
BanditRLProof.OFUL.matrixNorm_sq theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:60
BanditRLProof.OFUL.finiteHorizonResponseVector definition OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:68
BanditRLProof.OFUL.finiteHorizonRidgeEstimate definition OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:77
BanditRLProof.OFUL.finiteHorizonConfidenceThreshold definition OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:87
BanditRLProof.OFUL.finiteHorizonConfidenceRadius definition OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:100
BanditRLProof.OFUL.one_le_det_add_posSemidef_div_det theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:113
BanditRLProof.OFUL.finiteHorizonConfidenceThreshold_nonneg theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:130
BanditRLProof.OFUL.finiteHorizonResponseVector_eq_featureGram_mulVec_add_noiseScore theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:162
BanditRLProof.OFUL.posDef_nonsingInv_mulVec_mulVec theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:197
BanditRLProof.OFUL.posDef_mulVec_nonsingInv_mulVec theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:207
BanditRLProof.OFUL.matrixNorm_nonsingInv_mulVec_sq theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:219
BanditRLProof.OFUL.finiteHorizonRidgeEstimate_sub_eq_inverseScore_sub_inverseBias theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:232
BanditRLProof.OFUL.finiteHorizonRidgeEstimate_error_matrixNorm_le_score_add_bias theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:294
BanditRLProof.OFUL.selfNormalizedQuadratic_gt_of_ridgeEstimate_error_matrixNorm_gt_confidenceRadius theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:325
BanditRLProof.OFUL.measure_finiteHorizonRidgeEstimate_error_matrixNorm_gt_confidenceRadius_le theorem OFUL BanditRLProof.OFULConfidenceEllipsoid Compiled BanditRLProof/OFULConfidenceEllipsoid.lean:401
BanditRLProof.OFUL.rankOneGram definition OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:29
BanditRLProof.OFUL.rankOneGram_eq_replicateCol_mul_replicateRow theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:34
BanditRLProof.OFUL.rankOneGram_isHermitian theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:43
BanditRLProof.OFUL.det_one_add_rankOneGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:55
BanditRLProof.OFUL.det_rankOne_update_factor_eq_one_add_dotProduct_inv_mulVec theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:68
BanditRLProof.OFUL.det_add_rankOneGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:90
BanditRLProof.OFUL.det_scalar_identity theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:102
BanditRLProof.OFUL.det_scalar_identity_ne_zero theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:112
BanditRLProof.OFUL.isUnit_det_scalar_identity theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:123
BanditRLProof.OFUL.det_scalar_add_rankOneGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:136
BanditRLProof.OFUL.quadraticForm definition OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:151
BanditRLProof.OFUL.quadraticForm_add theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:158
BanditRLProof.OFUL.dotProduct_mulVec_eq_quadraticForm theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:195
BanditRLProof.OFUL.quadraticForm_scalar_identity theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:202
BanditRLProof.OFUL.sum_sq_pos_of_exists_ne_zero theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:224
BanditRLProof.OFUL.exists_coord_ne_zero_of_ne_zero theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:236
BanditRLProof.OFUL.featureGram definition OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:246
BanditRLProof.OFUL.featureGram_isHermitian theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:253
BanditRLProof.OFUL.regularizedFeatureGram definition OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:263
BanditRLProof.OFUL.regularizedFeatureGram_eq_scalar_add_featureGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:271
BanditRLProof.OFUL.regularizedFeatureGram_isHermitian theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:280
BanditRLProof.OFUL.prefixFeatureGram definition OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:291
BanditRLProof.OFUL.regularizedPrefixFeatureGram definition OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:297
BanditRLProof.OFUL.prefixFeatureGram_succ theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:304
BanditRLProof.OFUL.regularizedPrefixFeatureGram_succ theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:313
BanditRLProof.OFUL.prefixFeatureGram_zero theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:324
BanditRLProof.OFUL.regularizedPrefixFeatureGram_zero theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:331
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_zero theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:340
BanditRLProof.OFUL.prefixFeatureGram_isHermitian theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:349
BanditRLProof.OFUL.regularizedPrefixFeatureGram_isHermitian theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:358
BanditRLProof.OFUL.trace_rankOneGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:368
BanditRLProof.OFUL.trace_scalar_identity theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:375
BanditRLProof.OFUL.trace_prefixFeatureGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:384
BanditRLProof.OFUL.trace_regularizedPrefixFeatureGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:394
BanditRLProof.OFUL.trace_regularizedPrefixFeatureGram_le theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:408
BanditRLProof.OFUL.finset_prod_le_pow_sum_div_card_of_nonneg theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:424
BanditRLProof.OFUL.prod_univ_le_pow_sum_div_card_of_nonneg theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:448
BanditRLProof.OFUL.det_posSemidef_le_pow_trace_div_card theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:458
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_le_pow_trace_bound_average theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:475
BanditRLProof.OFUL.rankOneGram_quadraticForm_eq_sq theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:506
BanditRLProof.OFUL.rankOneGram_posSemidef theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:550
BanditRLProof.OFUL.rankOneGram_quadraticForm_nonneg theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:566
BanditRLProof.OFUL.featureGram_quadraticForm_eq_sum_sq theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:577
BanditRLProof.OFUL.prefixFeatureGram_quadraticForm_eq_sum_sq theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:632
BanditRLProof.OFUL.regularizedFeatureGram_quadraticForm_eq_sum_sq theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:687
BanditRLProof.OFUL.regularizedPrefixFeatureGram_quadraticForm_eq_sum_sq theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:706
BanditRLProof.OFUL.featureGram_quadraticForm_nonneg theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:722
BanditRLProof.OFUL.prefixFeatureGram_quadraticForm_nonneg theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:730
BanditRLProof.OFUL.regularizedFeatureGram_quadraticForm_nonneg theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:738
BanditRLProof.OFUL.regularizedPrefixFeatureGram_quadraticForm_nonneg theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:752
BanditRLProof.OFUL.regularizedFeatureGram_quadraticForm_pos_of_pos_lambda theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:768
BanditRLProof.OFUL.regularizedPrefixFeatureGram_quadraticForm_pos_of_pos_lambda theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:784
BanditRLProof.OFUL.regularizedFeatureGram_posDef theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:796
BanditRLProof.OFUL.regularizedPrefixFeatureGram_posDef theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:814
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_le_pow_trace_div_card theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:831
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_le_pow_trace_bound_average_of_pos_lambda theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:847
BanditRLProof.OFUL.regularizedPrefixFeatureGram_inv_posDef theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:870
BanditRLProof.OFUL.regularizedPrefixFeatureGram_inv_quadratic_nonneg theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:882
BanditRLProof.OFUL.regularizedFeatureGram_det_pos theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:899
BanditRLProof.OFUL.regularizedPrefixFeatureGram_det_pos theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:908
BanditRLProof.OFUL.regularizedFeatureGram_det_ne_zero theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:917
BanditRLProof.OFUL.regularizedPrefixFeatureGram_det_ne_zero theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:926
BanditRLProof.OFUL.isUnit_det_regularizedFeatureGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:937
BanditRLProof.OFUL.isUnit_det_regularizedPrefixFeatureGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:949
BanditRLProof.OFUL.det_regularizedFeatureGram_add_rankOneGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:964
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_add_rankOneGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:982
BanditRLProof.OFUL.regularizedFeatureGram_add_rankOneGram_posDef theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:995
BanditRLProof.OFUL.regularizedPrefixFeatureGram_add_rankOneGram_posDef theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1006
BanditRLProof.OFUL.det_regularizedFeatureGram_add_rankOneGram_pos theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1016
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_add_rankOneGram_pos theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1027
BanditRLProof.OFUL.regularizedFeatureGram_rankOne_update_factor_pos theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1037
BanditRLProof.OFUL.regularizedPrefixFeatureGram_rankOne_update_factor_pos theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1063
BanditRLProof.OFUL.log_det_regularizedFeatureGram_add_rankOneGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1088
BanditRLProof.OFUL.log_det_regularizedPrefixFeatureGram_add_rankOneGram theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1105
BanditRLProof.OFUL.log_det_regularizedFeatureGram_add_rankOneGram_sub theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1122
BanditRLProof.OFUL.log_det_regularizedPrefixFeatureGram_add_rankOneGram_sub theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1136
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_succ theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1150
BanditRLProof.OFUL.log_det_regularizedPrefixFeatureGram_succ_sub theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1165
BanditRLProof.OFUL.sum_range_forward_difference theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1180
BanditRLProof.OFUL.sum_range_log_update_factor_eq_log_det_ratio theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1197
BanditRLProof.OFUL.div_one_add_self_le_log_one_add theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1216
BanditRLProof.OFUL.self_le_two_log_one_add_of_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1234
BanditRLProof.OFUL.one_le_two_log_two theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1247
BanditRLProof.OFUL.min_one_le_two_log_one_add theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1254
BanditRLProof.OFUL.sum_range_min_one_le_two_sum_log_one_add theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1272
BanditRLProof.OFUL.sum_range_min_one_le_two_of_sum_log_one_add_le theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1292
BanditRLProof.OFUL.sum_range_le_two_sum_log_one_add_of_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1307
BanditRLProof.OFUL.sum_range_le_two_of_sum_log_one_add_le_of_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1330
BanditRLProof.OFUL.sum_range_log_regularizedPrefixFeatureGram_update_factor_eq_log_det_ratio theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1347
BanditRLProof.OFUL.sum_range_log_regularizedPrefixFeatureGram_update_factor_eq_log_det_sub_base theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1373
BanditRLProof.OFUL.sum_range_min_prefix_update_le_two_log_det_sub_base theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1395
BanditRLProof.OFUL.sum_range_prefix_update_le_two_log_det_sub_base theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1425
BanditRLProof.OFUL.sum_range_min_prefix_update_le_two_log_det_sub_base_of_pos_lambda theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1462
BanditRLProof.OFUL.sum_range_prefix_update_le_two_log_det_sub_base_of_update_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1486
BanditRLProof.OFUL.sum_range_min_prefix_update_le_two_log_det_upper theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1513
BanditRLProof.OFUL.sum_range_prefix_update_le_two_log_det_upper_of_update_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1537
BanditRLProof.OFUL.log_det_regularizedPrefixFeatureGram_sub_base_le_of_det_le_mul_exp theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1564
BanditRLProof.OFUL.sum_range_min_prefix_update_le_two_det_mul_exp_upper theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1591
BanditRLProof.OFUL.sum_range_prefix_update_le_two_det_mul_exp_upper_of_update_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1613
BanditRLProof.OFUL.trace_average_pow_le_lambda_pow_mul_exp_dim_scaled theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1644
BanditRLProof.OFUL.trace_average_pow_le_lambda_pow_mul_exp_log theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1705
BanditRLProof.OFUL.trace_average_exp_exponent_dim_cancel theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1755
BanditRLProof.OFUL.trace_average_pow_le_lambda_pow_mul_exp theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1770
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_le_mul_exp_of_trace_average_bound theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1787
BanditRLProof.OFUL.sum_range_min_prefix_update_le_two_of_trace_average_bound theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1806
BanditRLProof.OFUL.sum_range_prefix_update_le_two_of_trace_average_bound_of_update_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1834
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_le_mul_exp_trace_average_dim_scaled theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1877
BanditRLProof.OFUL.sum_range_min_prefix_update_le_two_trace_average_dim_scaled theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1900
BanditRLProof.OFUL.sum_range_prefix_update_le_two_trace_average_dim_scaled_of_update_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1926
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_le_mul_exp_trace_average theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1958
BanditRLProof.OFUL.det_regularizedPrefixFeatureGram_le_mul_exp_trace_average_log theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:1976
BanditRLProof.OFUL.sum_range_min_prefix_update_le_two_trace_average theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:2001
BanditRLProof.OFUL.sum_range_prefix_update_le_two_trace_average_of_update_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:2023
BanditRLProof.OFUL.sum_range_min_prefix_update_le_two_trace_average_log theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:2054
BanditRLProof.OFUL.sum_range_prefix_update_le_two_trace_average_log_of_update_le_one theorem OFUL BanditRLProof.OFULEllipticalPotential Compiled BanditRLProof/OFULEllipticalPotential.lean:2084
BanditRLProof.OFUL.standardLogDeterminantAndEllipticalPotential theorem OFUL BanditRLProof.OFULEllipticalPotentialFoundation Compiled BanditRLProof/OFULEllipticalPotentialFoundation.lean:25
BanditRLProof.OFUL.canonicalHistoryTrajectorySumRangeAllGap definition OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:18
BanditRLProof.OFUL.IsOptimalLinearArm definition OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:33
BanditRLProof.OFUL.canonicalHistoryTrajectorySumRangeAllFixedComparatorGap_nonneg theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:44
BanditRLProof.OFUL.measurable_canonicalHistoryTrajectorySumRangeAllGap theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:61
BanditRLProof.OFUL.abs_linearValue_sub_linearValue_le_two_mul_parameterFeatureBound theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:82
BanditRLProof.OFUL.standardScalarAllRoundGapEnvelope definition OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:105
BanditRLProof.OFUL.abs_canonicalHistoryTrajectorySumRangeAllGap_le_envelope theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:110
BanditRLProof.OFUL.standardScalarAllRoundGapEnvelope_nonneg theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:157
BanditRLProof.OFUL.standardScalarAllRoundGapBound_nonneg theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:165
BanditRLProof.OFUL.integrable_canonicalHistoryTrajectorySumRangeAllGap theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:185
BanditRLProof.OFUL.measurableSet_canonicalHistoryTrajectorySumRangeAllGapStandardViolationSet theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:211
BanditRLProof.OFUL.integral_canonicalHistoryTrajectorySumRangeAllGap_le_standard_add_envelope_mul_real_measure theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:231
BanditRLProof.OFUL.integral_canonicalHistoryTrajectorySumRangeAllGap_le_standard_add_envelope_mul_delta_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:322
BanditRLProof.OFUL.integral_canonicalHistoryTrajectorySumRangeAllFixedComparatorGap_le_standard_add_envelope_mul_delta_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:393
BanditRLProof.OFUL.integral_canonicalHistoryTrajectoryPseudoRegret_nonneg_and_le_standard_add_envelope_mul_delta_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:434
BanditRLProof.OFUL.standardExpectedRegretDelta definition OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:481
BanditRLProof.OFUL.standardExpectedRegretDelta_pos theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:484
BanditRLProof.OFUL.standardExpectedRegretDelta_le_one theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:489
BanditRLProof.OFUL.standardScalarAllRoundGapEnvelope_mul_standardExpectedRegretDelta theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:498
BanditRLProof.OFUL.integral_canonicalHistoryTrajectoryPseudoRegret_nonneg_and_le_standardExpectedBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULExpectedRegret Compiled BanditRLProof/OFULExpectedRegret.lean:515
BanditRLProof.OFUL.standardScalarLogDetBudget_isBigO_log theorem OFUL BanditRLProof.OFULExpectedRegretAsymptotics Compiled BanditRLProof/OFULExpectedRegretAsymptotics.lean:21
BanditRLProof.OFUL.standardExpectedRegretLogBudget_isBigO_log theorem OFUL BanditRLProof.OFULExpectedRegretAsymptotics Compiled BanditRLProof/OFULExpectedRegretAsymptotics.lean:80
BanditRLProof.OFUL.sqrt_log_succ_isBigO_log_succ theorem OFUL BanditRLProof.OFULExpectedRegretAsymptotics Compiled BanditRLProof/OFULExpectedRegretAsymptotics.lean:101
BanditRLProof.OFUL.standardExpectedPseudoRegretBound_isBigO_sqrt_mul_log theorem OFUL BanditRLProof.OFULExpectedRegretAsymptotics Compiled BanditRLProof/OFULExpectedRegretAsymptotics.lean:126
BanditRLProof.OFUL.canonicalStandardExpectedPseudoRegret definition OFUL BanditRLProof.OFULExpectedRegretAsymptotics Compiled BanditRLProof/OFULExpectedRegretAsymptotics.lean:247
BanditRLProof.OFUL.canonicalStandardExpectedPseudoRegret_nonneg_and_le theorem OFUL BanditRLProof.OFULExpectedRegretAsymptotics Compiled BanditRLProof/OFULExpectedRegretAsymptotics.lean:267
BanditRLProof.OFUL.canonicalStandardExpectedPseudoRegret_isBigO_sqrt_mul_log theorem OFUL BanditRLProof.OFULExpectedRegretAsymptotics Compiled BanditRLProof/OFULExpectedRegretAsymptotics.lean:296
BanditRLProof.OFUL.sqrt_mul_log_succ_isLittleO_natCast_succ theorem OFUL BanditRLProof.OFULExpectedRegretConsistency Compiled BanditRLProof/OFULExpectedRegretConsistency.lean:18
BanditRLProof.OFUL.standardExpectedPseudoRegretBound_isLittleO_natCast_succ theorem OFUL BanditRLProof.OFULExpectedRegretConsistency Compiled BanditRLProof/OFULExpectedRegretConsistency.lean:40
BanditRLProof.OFUL.canonicalStandardExpectedPseudoRegret_isLittleO_natCast_succ theorem OFUL BanditRLProof.OFULExpectedRegretConsistency Compiled BanditRLProof/OFULExpectedRegretConsistency.lean:53
BanditRLProof.OFUL.canonicalStandardExpectedAveragePseudoRegret definition OFUL BanditRLProof.OFULExpectedRegretConsistency Compiled BanditRLProof/OFULExpectedRegretConsistency.lean:79
BanditRLProof.OFUL.canonicalStandardExpectedAveragePseudoRegret_tendsto_zero theorem OFUL BanditRLProof.OFULExpectedRegretConsistency Compiled BanditRLProof/OFULExpectedRegretConsistency.lean:94
BanditRLProof.OFUL.standardExpectedRegretLogBudget definition OFUL BanditRLProof.OFULExpectedRegretRate Compiled BanditRLProof/OFULExpectedRegretRate.lean:21
BanditRLProof.OFUL.standardExpectedRegretAlgorithmDelta_eq_inv_sq theorem OFUL BanditRLProof.OFULExpectedRegretRate Compiled BanditRLProof/OFULExpectedRegretRate.lean:32
BanditRLProof.OFUL.standardScalarConfidenceRadiusUpper_standardExpectedRegret theorem OFUL BanditRLProof.OFULExpectedRegretRate Compiled BanditRLProof/OFULExpectedRegretRate.lean:45
BanditRLProof.OFUL.standardExpectedPseudoRegretBound definition OFUL BanditRLProof.OFULExpectedRegretRate Compiled BanditRLProof/OFULExpectedRegretRate.lean:110
BanditRLProof.OFUL.standardScalarAllRoundGapBound_add_initial_eq_standardExpectedPseudoRegretBound theorem OFUL BanditRLProof.OFULExpectedRegretRate Compiled BanditRLProof/OFULExpectedRegretRate.lean:126
BanditRLProof.OFUL.integral_canonicalHistoryTrajectoryPseudoRegret_nonneg_and_le_explicitStandardExpectedBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULExpectedRegretRate Compiled BanditRLProof/OFULExpectedRegretRate.lean:152
BanditRLProof.OFUL.confidenceWidth definition OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:18
BanditRLProof.OFUL.linearValue definition OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:24
BanditRLProof.OFUL.optimisticScore definition OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:30
BanditRLProof.OFUL.finiteActionArgmax definition OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:38
BanditRLProof.OFUL.finiteActionArgmax_spec theorem OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:44
BanditRLProof.OFUL.abs_dotProduct_le_matrixNorm_mul_confidenceWidth theorem OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:54
BanditRLProof.OFUL.linearValue_le_optimisticScore_of_matrixNorm_sub_le theorem OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:93
BanditRLProof.OFUL.optimisticScore_le_linearValue_add_two_mul_bonus_of_matrixNorm_sub_le theorem OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:120
BanditRLProof.OFUL.finiteActionOptimisticChoice definition OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:145
BanditRLProof.OFUL.finiteActionOptimisticChoice_score_max theorem OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:155
BanditRLProof.OFUL.linearValue_sub_finiteActionOptimisticChoice_le_two_mul_bonus theorem OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:174
BanditRLProof.OFUL.finiteHorizonScalarGram definition OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:212
BanditRLProof.OFUL.finiteHorizonScalarOptimisticAction definition OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:223
BanditRLProof.OFUL.finiteHorizonScalarOptimisticAction_gap_le theorem OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:244
BanditRLProof.OFUL.finiteHorizonScalarOptimismViolationSet definition OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:295
BanditRLProof.OFUL.measure_finiteHorizonScalarOptimismViolationSet_le theorem OFUL BanditRLProof.OFULFiniteActionOptimism Compiled BanditRLProof/OFULFiniteActionOptimism.lean:325
BanditRLProof.OFUL.finiteHorizonNoiseScore definition OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:20
BanditRLProof.OFUL.varianceWeightedFeature definition OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:29
BanditRLProof.OFUL.finiteHorizonVarianceGram definition OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:36
BanditRLProof.OFUL.inner_finiteHorizonNoiseScore_eq_sum_projection_mul_noise theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:45
BanditRLProof.OFUL.finiteHorizonVarianceGram_quadraticForm_eq_sum theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:71
BanditRLProof.OFUL.finiteHorizonVarianceGram_posSemidef theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:100
BanditRLProof.OFUL.measurable_finiteHorizonVarianceGram_apply theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:119
BanditRLProof.OFUL.measurable_finiteHorizonNoiseScore theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:135
BanditRLProof.OFUL.compensatedScore_eq_inner_sub_varianceGram theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:150
BanditRLProof.OFUL.finiteHorizonScoreVarianceGram_hasMGFUpperBoundAt theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:180
BanditRLProof.OFUL.integral_exp_inner_finiteHorizonScore_sub_varianceGram_le_one theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:257
BanditRLProof.OFUL.integral_gaussianQuadraticExponential_finiteHorizon_le_one theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:299
BanditRLProof.OFUL.lintegral_gaussianQuadraticExponentialENNReal_finiteHorizon_prod_le_one theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:338
BanditRLProof.OFUL.lintegral_gaussianQuadraticExponentialENNReal_finiteHorizon_prod_multivariateGaussian_zero_inv_le_one theorem OFUL BanditRLProof.OFULFiniteHorizonScoreGram Compiled BanditRLProof/OFULFiniteHorizonScoreGram.lean:456
BanditRLProof.OFUL.inner_toEuclideanCLM_selfAdjoint theorem OFUL BanditRLProof.OFULGaussianCovarianceMixture Compiled BanditRLProof/OFULGaussianCovarianceMixture.lean:20
BanditRLProof.OFUL.inner_toEuclideanCLM_congruence theorem OFUL BanditRLProof.OFULGaussianCovarianceMixture Compiled BanditRLProof/OFULGaussianCovarianceMixture.lean:35
BanditRLProof.OFUL.integral_exp_inner_sub_quadratic_multivariateGaussian_zero_inv_transformed theorem OFUL BanditRLProof.OFULGaussianCovarianceMixture Compiled BanditRLProof/OFULGaussianCovarianceMixture.lean:57
BanditRLProof.OFUL.sqrt_inv_congruence_factorization theorem OFUL BanditRLProof.OFULGaussianCovarianceMixture Compiled BanditRLProof/OFULGaussianCovarianceMixture.lean:103
BanditRLProof.OFUL.det_one_add_sqrt_inv_congruence_eq_ratio theorem OFUL BanditRLProof.OFULGaussianCovarianceMixture Compiled BanditRLProof/OFULGaussianCovarianceMixture.lean:130
BanditRLProof.OFUL.sqrt_inv_congruence_inverse theorem OFUL BanditRLProof.OFULGaussianCovarianceMixture Compiled BanditRLProof/OFULGaussianCovarianceMixture.lean:162
BanditRLProof.OFUL.dotProduct_sqrt_inv_congruence_inverse theorem OFUL BanditRLProof.OFULGaussianCovarianceMixture Compiled BanditRLProof/OFULGaussianCovarianceMixture.lean:187
BanditRLProof.OFUL.integral_exp_inner_sub_quadratic_multivariateGaussian_zero_inv_detRatio theorem OFUL BanditRLProof.OFULGaussianCovarianceMixture Compiled BanditRLProof/OFULGaussianCovarianceMixture.lean:222
BanditRLProof.OFUL.integral_exp_inner_sub_quadratic_multivariateGaussian_zero_inv theorem OFUL BanditRLProof.OFULGaussianCovarianceMixture Compiled BanditRLProof/OFULGaussianCovarianceMixture.lean:240
BanditRLProof.OFUL.integrable_exp_inner_sub_quadratic_multivariateGaussian_zero_inv theorem OFUL BanditRLProof.OFULGaussianEvaluatedMixture Compiled BanditRLProof/OFULGaussianEvaluatedMixture.lean:23
BanditRLProof.OFUL.lintegral_gaussianQuadraticExponentialENNReal_multivariateGaussian_zero_inv theorem OFUL BanditRLProof.OFULGaussianEvaluatedMixture Compiled BanditRLProof/OFULGaussianEvaluatedMixture.lean:103
BanditRLProof.OFUL.finiteHorizonDetRatioInvGramExponential definition OFUL BanditRLProof.OFULGaussianEvaluatedMixture Compiled BanditRLProof/OFULGaussianEvaluatedMixture.lean:128
BanditRLProof.OFUL.lintegral_gaussianQuadraticExponentialENNReal_finiteHorizon_multivariateGaussian_zero_inv theorem OFUL BanditRLProof.OFULGaussianEvaluatedMixture Compiled BanditRLProof/OFULGaussianEvaluatedMixture.lean:151
BanditRLProof.OFUL.measurable_finiteHorizonDetRatioInvGramExponential theorem OFUL BanditRLProof.OFULGaussianEvaluatedMixture Compiled BanditRLProof/OFULGaussianEvaluatedMixture.lean:180
BanditRLProof.OFUL.lintegral_finiteHorizon_detRatio_invGramExponential_le_one theorem OFUL BanditRLProof.OFULGaussianEvaluatedMixture Compiled BanditRLProof/OFULGaussianEvaluatedMixture.lean:230
BanditRLProof.OFUL.integral_exp_linear_sub_quadratic_gaussianReal_zero_one theorem OFUL BanditRLProof.OFULGaussianMixture Compiled BanditRLProof/OFULGaussianMixture.lean:27
BanditRLProof.OFUL.integral_exp_sum_linear_sub_diagonal_quadratic_pi_gaussianReal theorem OFUL BanditRLProof.OFULGaussianMixture Compiled BanditRLProof/OFULGaussianMixture.lean:120
BanditRLProof.OFUL.integral_exp_sum_linear_sub_diagonal_quadratic_pi_gaussianReal_eq theorem OFUL BanditRLProof.OFULGaussianMixture Compiled BanditRLProof/OFULGaussianMixture.lean:161
BanditRLProof.OFUL.integral_exp_sum_linear_sub_diagonal_quadratic_pi_gaussianReal_det theorem OFUL BanditRLProof.OFULGaussianMixture Compiled BanditRLProof/OFULGaussianMixture.lean:187
BanditRLProof.OFUL.gaussianQuadraticExponential definition OFUL BanditRLProof.OFULGaussianMixtureMeasurability Compiled BanditRLProof/OFULGaussianMixtureMeasurability.lean:24
BanditRLProof.OFUL.measurable_gaussianQuadraticExponential_dot theorem OFUL BanditRLProof.OFULGaussianMixtureMeasurability Compiled BanditRLProof/OFULGaussianMixtureMeasurability.lean:33
BanditRLProof.OFUL.measurable_gaussianQuadraticExponential theorem OFUL BanditRLProof.OFULGaussianMixtureMeasurability Compiled BanditRLProof/OFULGaussianMixtureMeasurability.lean:51
BanditRLProof.OFUL.gaussianQuadraticExponentialENNReal definition OFUL BanditRLProof.OFULGaussianMixtureMeasurability Compiled BanditRLProof/OFULGaussianMixtureMeasurability.lean:68
BanditRLProof.OFUL.measurable_gaussianQuadraticExponentialENNReal theorem OFUL BanditRLProof.OFULGaussianMixtureMeasurability Compiled BanditRLProof/OFULGaussianMixtureMeasurability.lean:75
BanditRLProof.OFUL.lintegral_gaussianQuadraticExponentialENNReal_prod theorem OFUL BanditRLProof.OFULGaussianMixtureMeasurability Compiled BanditRLProof/OFULGaussianMixtureMeasurability.lean:84
BanditRLProof.OFUL.lintegral_gaussianQuadraticExponentialENNReal_prod_multivariateGaussian_zero_inv theorem OFUL BanditRLProof.OFULGaussianMixtureMeasurability Compiled BanditRLProof/OFULGaussianMixtureMeasurability.lean:99
BanditRLProof.OFUL.inner_sum_smul_orthonormalBasis theorem OFUL BanditRLProof.OFULGaussianSpectralMixture Compiled BanditRLProof/OFULGaussianSpectralMixture.lean:20
BanditRLProof.OFUL.inner_sum_smul_orthonormalBasis_left theorem OFUL BanditRLProof.OFULGaussianSpectralMixture Compiled BanditRLProof/OFULGaussianSpectralMixture.lean:28
BanditRLProof.OFUL.inner_toEuclideanCLM_sum_eigenvectorBasis theorem OFUL BanditRLProof.OFULGaussianSpectralMixture Compiled BanditRLProof/OFULGaussianSpectralMixture.lean:39
BanditRLProof.OFUL.integral_exp_inner_sub_quadratic_stdGaussian_eigenvalues theorem OFUL BanditRLProof.OFULGaussianSpectralMixture Compiled BanditRLProof/OFULGaussianSpectralMixture.lean:108
BanditRLProof.OFUL.det_one_add_posSemidef_eq_prod_eigenvalues theorem OFUL BanditRLProof.OFULGaussianSpectralMixture Compiled BanditRLProof/OFULGaussianSpectralMixture.lean:175
BanditRLProof.OFUL.toEuclideanCLM_one_add_posSemidef_inv_eigenvectorBasis theorem OFUL BanditRLProof.OFULGaussianSpectralMixture Compiled BanditRLProof/OFULGaussianSpectralMixture.lean:233
BanditRLProof.OFUL.dotProduct_one_add_posSemidef_inv_mulVec_eq_sum_eigenvalues theorem OFUL BanditRLProof.OFULGaussianSpectralMixture Compiled BanditRLProof/OFULGaussianSpectralMixture.lean:285
BanditRLProof.OFUL.integral_exp_inner_sub_quadratic_stdGaussian_det theorem OFUL BanditRLProof.OFULGaussianSpectralMixture Compiled BanditRLProof/OFULGaussianSpectralMixture.lean:351
BanditRLProof.OFUL.linearValue_sub_selected_le_two_mul_bonus_of_score_max theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:25
BanditRLProof.OFUL.finiteHistoryScalarRidgeOptimisticAction_gap_le theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:56
BanditRLProof.OFUL.canonicalHistoryTrajectoryFeature definition OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:113
BanditRLProof.OFUL.canonicalHistoryTrajectoryResponse definition OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:121
BanditRLProof.OFUL.finiteHistoryObservedFeature_finitePairHistoryOfTrace_of_le theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:127
BanditRLProof.OFUL.finiteHistoryObservedResponse_finitePairHistoryOfTrace_of_le theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:138
BanditRLProof.OFUL.finiteHorizonFeatureGram_finitePairHistoryOfTrace_eq theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:151
BanditRLProof.OFUL.finiteHorizonResponseVector_finitePairHistoryOfTrace_eq theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:178
BanditRLProof.OFUL.finiteHistoryScalarRidgeDesign_finitePairHistoryOfTrace_eq theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:206
BanditRLProof.OFUL.finiteHistoryScalarRidgeEstimate_finitePairHistoryOfTrace_eq theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:223
BanditRLProof.OFUL.finiteHistoryScalarRidgeRadius_finitePairHistoryOfTrace_eq theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:243
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_succ_gap_le_of_not_mem_confidenceFailure theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:268
BanditRLProof.OFUL.canonicalHistoryTrajectory_sum_range_succ_gap_le_on_uniformConfidence theorem OFUL BanditRLProof.OFULGeneratedTrajectoryConfidenceGap Compiled BanditRLProof/OFULGeneratedTrajectoryConfidenceGap.lean:371
BanditRLProof.OFUL.canonicalHistoryTrajectoryBeforeFiltration definition OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:28
BanditRLProof.OFUL.canonicalHistoryTrajectoryBeforeFiltration_zero theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:56
BanditRLProof.OFUL.canonicalHistoryTrajectoryBeforeFiltration_succ theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:62
BanditRLProof.OFUL.measurable_finiteHistoryScalarRidgeOptimisticAction theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:69
BanditRLProof.OFUL.canonicalHistoryTrajectoryPredictableFeature definition OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:98
BanditRLProof.OFUL.canonicalHistoryTrajectoryPredictableFeature_stronglyMeasurable theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:114
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_zero_ae_eq_initialArm theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:159
BanditRLProof.OFUL.canonicalHistoryTrajectoryFeature_ae_eq_predictableFeature theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:213
BanditRLProof.OFUL.canonicalHistoryTrajectoryFeature_ae_eq_predictableFeature_all theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:249
BanditRLProof.OFUL.canonicalHistoryTrajectoryPredictableResidual definition OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:273
BanditRLProof.OFUL.measurable_canonicalHistoryTrajectoryResponse_before_succ theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:288
BanditRLProof.OFUL.canonicalHistoryTrajectoryPredictableResidual_stronglyAdapted theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:313
BanditRLProof.OFUL.finiteActionProjectionBound definition OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:371
BanditRLProof.OFUL.finiteActionProjectionBound_nonneg theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:383
BanditRLProof.OFUL.predictableFeature_projection_le_finiteActionProjectionBound theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:403
BanditRLProof.OFUL.CanonicalPredictableScalarRidgeResidualLaw structure OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:447
BanditRLProof.OFUL.mem_scalarRidgeConfidenceFailureAt_iff_of_feature_eq theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:471
BanditRLProof.OFUL.mem_finiteHorizonUniformScalarRidgeConfidenceFailureSet_iff_of_feature_eq theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:510
BanditRLProof.OFUL.measure_canonicalHistoryTrajectory_uniformScalarRidgeConfidenceFailureSet_le_of_predictableResidualLaw theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:549
BanditRLProof.OFUL.measure_canonicalHistoryTrajectorySumRangeSuccGapViolationSet_le_of_predictableResidualLaw theorem OFUL BanditRLProof.OFULGeneratedTrajectoryPredictableConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryPredictableConfidence.lean:661
BanditRLProof.OFUL.standardScalarLogDetBudget definition OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:21
BanditRLProof.OFUL.standardScalarConfidenceRadiusUpper definition OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:34
BanditRLProof.OFUL.standardSelectedWidthBudget definition OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:48
BanditRLProof.OFUL.standardScalarRadiusWidthBound definition OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:58
BanditRLProof.OFUL.finiteHorizonScalarGram_eq_regularizedPrefixFeatureGram theorem OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:68
BanditRLProof.OFUL.standardScalarLogDetBudget_mono theorem OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:79
BanditRLProof.OFUL.standardScalarLogDetBudget_nonneg theorem OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:118
BanditRLProof.OFUL.finiteHorizonScalarConfidenceRadius_le_standardUpper theorem OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:142
BanditRLProof.OFUL.standardScalarConfidenceRadiusUpper_nonneg theorem OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:251
BanditRLProof.OFUL.standardSelectedWidthBudget_nonneg theorem OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:261
BanditRLProof.OFUL.canonicalHistoryTrajectory_sum_range_succ_radius_mul_width_le_standard theorem OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:273
BanditRLProof.OFUL.canonicalHistoryTrajectorySumRangeSuccGapStandardViolationSet definition OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:432
BanditRLProof.OFUL.canonicalHistoryTrajectorySumRangeSuccGapStandardViolationSet_subset theorem OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:458
BanditRLProof.OFUL.measure_canonicalHistoryTrajectorySumRangeSuccGapStandardViolationSet_le_of_linearSubgaussianEnvironment theorem OFUL BanditRLProof.OFULGeneratedTrajectoryRadiusWidth Compiled BanditRLProof/OFULGeneratedTrajectoryRadiusWidth.lean:524
BanditRLProof.OFUL.CanonicalScalarRidgeConfidenceSource structure OFUL BanditRLProof.OFULGeneratedTrajectoryUniformConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryUniformConfidence.lean:28
BanditRLProof.OFUL.measure_canonicalHistoryTrajectory_uniformScalarRidgeConfidenceFailureSet_le theorem OFUL BanditRLProof.OFULGeneratedTrajectoryUniformConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryUniformConfidence.lean:72
BanditRLProof.OFUL.canonicalHistoryTrajectorySumRangeSuccGapViolationSet definition OFUL BanditRLProof.OFULGeneratedTrajectoryUniformConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryUniformConfidence.lean:116
BanditRLProof.OFUL.measure_canonicalHistoryTrajectorySumRangeSuccGapViolationSet_le theorem OFUL BanditRLProof.OFULGeneratedTrajectoryUniformConfidence Compiled BanditRLProof/OFULGeneratedTrajectoryUniformConfidence.lean:153
BanditRLProof.OFUL.standardHighProbabilityRegretLogBudget definition OFUL BanditRLProof.OFULHighProbabilityRegretRate Compiled BanditRLProof/OFULHighProbabilityRegretRate.lean:22
BanditRLProof.OFUL.standardScalarConfidenceRadiusUpper_highProbabilityRegret theorem OFUL BanditRLProof.OFULHighProbabilityRegretRate Compiled BanditRLProof/OFULHighProbabilityRegretRate.lean:34
BanditRLProof.OFUL.standardHighProbabilityPseudoRegretBound definition OFUL BanditRLProof.OFULHighProbabilityRegretRate Compiled BanditRLProof/OFULHighProbabilityRegretRate.lean:98
BanditRLProof.OFUL.standardScalarAllRoundGapBound_eq_standardHighProbabilityPseudoRegretBound theorem OFUL BanditRLProof.OFULHighProbabilityRegretRate Compiled BanditRLProof/OFULHighProbabilityRegretRate.lean:114
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret definition OFUL BanditRLProof.OFULHighProbabilityRegretRate Compiled BanditRLProof/OFULHighProbabilityRegretRate.lean:134
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret_nonneg_and_tail_le_explicitBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULHighProbabilityRegretRate Compiled BanditRLProof/OFULHighProbabilityRegretRate.lean:150
BanditRLProof.OFUL.canonicalHistoryTrajectory_initialReward_map_eq_historyAlgorithmInitialFeedback theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:24
BanditRLProof.OFUL.canonicalHistoryTrajectory_reward_succ_condDistrib_eq_historyStepReward theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:61
BanditRLProof.OFUL.canonicalHistoryTrajectory_reward_succ_condExpKernel_map_eq_historyStepReward_comap theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:117
BanditRLProof.OFUL.canonicalHistoryTrajectory_initialReward_condExpKernel_map_eq_historyAlgorithmInitialFeedback_unitComap theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:170
BanditRLProof.OFUL.finiteHistoryScalarRidge_historyStepKernel_map_snd theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:244
BanditRLProof.OFUL.canonicalHistoryTrajectory_initialReward_map_eq_scalarRidgeInitialFeedback theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:288
BanditRLProof.OFUL.canonicalHistoryTrajectory_reward_succ_condDistrib_eq_scalarRidgeStepReward theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:333
BanditRLProof.OFUL.canonicalHistoryTrajectory_reward_succ_condExpKernel_map_eq_scalarRidgeStepReward_comap theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:403
BanditRLProof.OFUL.canonicalHistoryTrajectory_initialReward_condExpKernel_map_eq_scalarRidgeInitialFeedback_unitComap theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:469
BanditRLProof.OFUL.CanonicalLinearSubgaussianEnvironmentLaw structure OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:554
BanditRLProof.OFUL.canonicalPredictableScalarRidgeResidualLaw_of_linearSubgaussianEnvironment definition OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:582
BanditRLProof.OFUL.measure_canonicalHistoryTrajectorySumRangeSuccGapViolationSet_le_of_linearSubgaussianEnvironment theorem OFUL BanditRLProof.OFULHistoryEnvironmentRewardLaw Compiled BanditRLProof/OFULHistoryEnvironmentRewardLaw.lean:787
BanditRLProof.OFUL.abs_linearValue_le_euclideanLength_mul_euclideanLength theorem OFUL BanditRLProof.OFULInitialRoundGap Compiled BanditRLProof/OFULInitialRoundGap.lean:19
BanditRLProof.OFUL.abs_linearValue_le_parameterFeatureBound theorem OFUL BanditRLProof.OFULInitialRoundGap Compiled BanditRLProof/OFULInitialRoundGap.lean:40
BanditRLProof.OFUL.linearValue_sub_linearValue_le_two_mul_parameterFeatureBound theorem OFUL BanditRLProof.OFULInitialRoundGap Compiled BanditRLProof/OFULInitialRoundGap.lean:54
BanditRLProof.OFUL.standardScalarInitialGapBound definition OFUL BanditRLProof.OFULInitialRoundGap Compiled BanditRLProof/OFULInitialRoundGap.lean:72
BanditRLProof.OFUL.canonicalHistoryTrajectory_initialGap_le_ae theorem OFUL BanditRLProof.OFULInitialRoundGap Compiled BanditRLProof/OFULInitialRoundGap.lean:80
BanditRLProof.OFUL.standardScalarAllRoundGapBound definition OFUL BanditRLProof.OFULInitialRoundGap Compiled BanditRLProof/OFULInitialRoundGap.lean:117
BanditRLProof.OFUL.canonicalHistoryTrajectorySumRangeAllGapStandardViolationSet definition OFUL BanditRLProof.OFULInitialRoundGap Compiled BanditRLProof/OFULInitialRoundGap.lean:127
BanditRLProof.OFUL.canonicalHistoryTrajectorySumRangeAllGapStandardViolationSet_ae_le_succ theorem OFUL BanditRLProof.OFULInitialRoundGap Compiled BanditRLProof/OFULInitialRoundGap.lean:150
BanditRLProof.OFUL.measure_canonicalHistoryTrajectorySumRangeAllGapStandardViolationSet_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULInitialRoundGap Compiled BanditRLProof/OFULInitialRoundGap.lean:211
BanditRLProof.OFUL.finiteHistoryOptimisticScore definition OFUL BanditRLProof.OFULMeasurableRecursiveSelection Compiled BanditRLProof/OFULMeasurableRecursiveSelection.lean:23
BanditRLProof.OFUL.finiteHistoryOptimisticAction definition OFUL BanditRLProof.OFULMeasurableRecursiveSelection Compiled BanditRLProof/OFULMeasurableRecursiveSelection.lean:46
BanditRLProof.OFUL.finiteHistoryOptimisticAction_score_max theorem OFUL BanditRLProof.OFULMeasurableRecursiveSelection Compiled BanditRLProof/OFULMeasurableRecursiveSelection.lean:67
BanditRLProof.OFUL.measurable_finiteHistoryOptimisticAction theorem OFUL BanditRLProof.OFULMeasurableRecursiveSelection Compiled BanditRLProof/OFULMeasurableRecursiveSelection.lean:97
BanditRLProof.OFUL.finiteHistoryOptimisticAlgorithm definition OFUL BanditRLProof.OFULMeasurableRecursiveSelection Compiled BanditRLProof/OFULMeasurableRecursiveSelection.lean:126
BanditRLProof.OFUL.finiteHistoryOptimisticAlgorithm_policy_apply theorem OFUL BanditRLProof.OFULMeasurableRecursiveSelection Compiled BanditRLProof/OFULMeasurableRecursiveSelection.lean:155
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_succ_ae_eq_finiteHistoryOptimisticAction theorem OFUL BanditRLProof.OFULMeasurableRecursiveSelection Compiled BanditRLProof/OFULMeasurableRecursiveSelection.lean:187
BanditRLProof.OFUL.finiteHistoryOptimisticSelectedFeature definition OFUL BanditRLProof.OFULMeasurableRecursiveSelection Compiled BanditRLProof/OFULMeasurableRecursiveSelection.lean:276
BanditRLProof.OFUL.canonicalHistoryTrajectory_candidateFeature_succ_ae_eq_selectedFeature theorem OFUL BanditRLProof.OFULMeasurableRecursiveSelection Compiled BanditRLProof/OFULMeasurableRecursiveSelection.lean:301
BanditRLProof.OFUL.regularizedPrefixFeatureGram_inv_quadratic_le_one theorem OFUL BanditRLProof.OFULNormalizedRadiusWidth Compiled BanditRLProof/OFULNormalizedRadiusWidth.lean:18
BanditRLProof.OFUL.confidenceWidth_regularizedPrefixFeatureGram_le_one theorem OFUL BanditRLProof.OFULNormalizedRadiusWidth Compiled BanditRLProof/OFULNormalizedRadiusWidth.lean:80
BanditRLProof.OFUL.canonicalHistoryTrajectory_confidenceWidth_le_one theorem OFUL BanditRLProof.OFULNormalizedRadiusWidth Compiled BanditRLProof/OFULNormalizedRadiusWidth.lean:92
BanditRLProof.OFUL.canonicalHistoryTrajectory_sum_range_succ_radius_mul_width_le_standard_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULNormalizedRadiusWidth Compiled BanditRLProof/OFULNormalizedRadiusWidth.lean:120
BanditRLProof.OFUL.measure_canonicalHistoryTrajectorySumRangeSuccGapStandardViolationSet_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULNormalizedRadiusWidth Compiled BanditRLProof/OFULNormalizedRadiusWidth.lean:158
BanditRLProof.OFUL.euclideanLength definition OFUL BanditRLProof.OFULScalarRegularizationBias Compiled BanditRLProof/OFULScalarRegularizationBias.lean:18
BanditRLProof.OFUL.scalarIdentity_posDef theorem OFUL BanditRLProof.OFULScalarRegularizationBias Compiled BanditRLProof/OFULScalarRegularizationBias.lean:23
BanditRLProof.OFUL.matrixNorm_nonsingInv_scalar_mulVec_le_sqrt_mul_euclideanLength theorem OFUL BanditRLProof.OFULScalarRegularizationBias Compiled BanditRLProof/OFULScalarRegularizationBias.lean:34
BanditRLProof.OFUL.finiteHorizonScalarConfidenceRadius definition OFUL BanditRLProof.OFULScalarRegularizationBias Compiled BanditRLProof/OFULScalarRegularizationBias.lean:161
BanditRLProof.OFUL.finiteHorizon_scalarRegularizationBias_le theorem OFUL BanditRLProof.OFULScalarRegularizationBias Compiled BanditRLProof/OFULScalarRegularizationBias.lean:173
BanditRLProof.OFUL.measure_finiteHorizonScalarRidgeEstimate_error_matrixNorm_gt_confidenceRadius_le theorem OFUL BanditRLProof.OFULScalarRegularizationBias Compiled BanditRLProof/OFULScalarRegularizationBias.lean:199
BanditRLProof.OFUL.squareIntegrableFiniteStoppingTime_of_bounded_ae theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:32
BanditRLProof.OFUL.stoppingTimeRoundSecondMoment_le_sq_of_bounded_ae theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:63
BanditRLProof.Budget.budgetExhaustionTime_le_reachHorizon_ae_of_spent_reach theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:110
BanditRLProof.Budget.squareIntegrableFiniteStoppingTime_budgetExhaustionTime_of_reachHorizon_ae theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:129
BanditRLProof.Budget.stoppingTimeRoundSecondMoment_budgetExhaustionTime_le_of_reachHorizon_ae theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:152
BanditRLProof.Budget.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_reachHorizonRoundsSq_add_initialGap_mul_reachHorizonRounds_mul_sqrt_delta_and_stoppedViolation_measure_le_of_budgetExhaustionTime_reachedBy_ae theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:181
BanditRLProof.Budget.AlignedWindowPositiveActionCostAE definition OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:280
BanditRLProof.Budget.alignedWindowPositiveActionCostAE_iff_forall_ae theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:294
BanditRLProof.Budget.canonicalActionCostProcess_alignedWindowPositive_ae theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:311
BanditRLProof.Budget.budget_le_cumulativeActionCost_budget_mul_ae theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:342
BanditRLProof.Budget.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_budgetWindowRoundsSq_add_initialGap_mul_budgetWindowRounds_mul_sqrt_delta_and_stoppedViolation_measure_le_of_aeAlignedWindowPositiveActionCostBudgetExhaustionTime theorem OFUL BanditRLProof.OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledAEAlignedWindowPositiveActionCostBudgetExhaustionExpectedRegret.lean:379
BanditRLProof.OFUL.telescopingStandardScalarAllRoundGapBound definition OFUL BanditRLProof.OFULScheduledAllHorizonAllRoundGap Compiled BanditRLProof/OFULScheduledAllHorizonAllRoundGap.lean:21
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectory_initialGap_le_ae theorem OFUL BanditRLProof.OFULScheduledAllHorizonAllRoundGap Compiled BanditRLProof/OFULScheduledAllHorizonAllRoundGap.lean:32
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectoryAllHorizonAllRoundGapStandardViolationSet definition OFUL BanditRLProof.OFULScheduledAllHorizonAllRoundGap Compiled BanditRLProof/OFULScheduledAllHorizonAllRoundGap.lean:72
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectoryAllHorizonAllRoundGapStandardViolationSet_subset_succ_ae theorem OFUL BanditRLProof.OFULScheduledAllHorizonAllRoundGap Compiled BanditRLProof/OFULScheduledAllHorizonAllRoundGap.lean:95
BanditRLProof.OFUL.measure_telescopingCanonicalHistoryTrajectoryAllHorizonAllRoundGapStandardViolationSet_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledAllHorizonAllRoundGap Compiled BanditRLProof/OFULScheduledAllHorizonAllRoundGap.lean:136
BanditRLProof.OFUL.telescopingCanonicalStandardHighProbabilityPseudoRegretAllHorizonViolationSet definition OFUL BanditRLProof.OFULScheduledAllHorizonAllRoundGap Compiled BanditRLProof/OFULScheduledAllHorizonAllRoundGap.lean:187
BanditRLProof.OFUL.telescopingCanonicalStandardHighProbabilityPseudoRegret_nonneg_and_allHorizon_tail_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledAllHorizonAllRoundGap Compiled BanditRLProof/OFULScheduledAllHorizonAllRoundGap.lean:209
BanditRLProof.OFUL.allTimeTelescopingDelta_antitone theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:22
BanditRLProof.OFUL.standardScalarConfidenceRadiusUpper_antitone_delta theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:42
BanditRLProof.OFUL.finiteHorizonScalarConfidenceRadius_telescoping_le_standardUpper_of_indices theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:119
BanditRLProof.OFUL.finiteHorizonScalarConfidenceRadius_telescoping_le_standardUpper theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:165
BanditRLProof.OFUL.telescopingStandardScalarRadiusWidthBound definition OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:189
BanditRLProof.OFUL.canonicalHistoryTrajectory_sum_range_succ_telescoping_radius_mul_width_le_standard theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:201
BanditRLProof.OFUL.canonicalHistoryTrajectory_sum_range_succ_telescoping_radius_mul_width_le_standard_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:355
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectory_sum_range_succ_gap_le_radius_mul_width_ae theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:395
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectory_sum_range_succ_gap_le_standard_ae_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:493
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectoryAllHorizonSuccGapStandardViolationSet definition OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:541
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectoryAllHorizonSuccGapStandardViolationSet_subset_confidenceFailure_ae theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:565
BanditRLProof.OFUL.measure_telescopingCanonicalHistoryTrajectoryAllHorizonSuccGapStandardViolationSet_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledAllHorizonCumulativeGap Compiled BanditRLProof/OFULScheduledAllHorizonCumulativeGap.lean:630
BanditRLProof.OFUL.telescopingHighProbabilityRegretLogBudget definition OFUL BanditRLProof.OFULScheduledAllHorizonHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledAllHorizonHighProbabilityRegretRate.lean:22
BanditRLProof.OFUL.telescopingHighProbabilityPseudoRegretBound definition OFUL BanditRLProof.OFULScheduledAllHorizonHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledAllHorizonHighProbabilityRegretRate.lean:35
BanditRLProof.OFUL.allTimeTelescopingDelta_eq_outerBudget_div_succ theorem OFUL BanditRLProof.OFULScheduledAllHorizonHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledAllHorizonHighProbabilityRegretRate.lean:54
BanditRLProof.OFUL.standardHighProbabilityRegretLogBudget_outerBudget_eq_telescoping theorem OFUL BanditRLProof.OFULScheduledAllHorizonHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledAllHorizonHighProbabilityRegretRate.lean:66
BanditRLProof.OFUL.standardHighProbabilityPseudoRegretBound_outerBudget_eq_telescoping theorem OFUL BanditRLProof.OFULScheduledAllHorizonHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledAllHorizonHighProbabilityRegretRate.lean:90
BanditRLProof.OFUL.telescopingStandardScalarAllRoundGapBound_eq_telescopingHighProbabilityPseudoRegretBound theorem OFUL BanditRLProof.OFULScheduledAllHorizonHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledAllHorizonHighProbabilityRegretRate.lean:111
BanditRLProof.OFUL.telescopingCanonicalExplicitHighProbabilityPseudoRegretAllHorizonViolationSet definition OFUL BanditRLProof.OFULScheduledAllHorizonHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledAllHorizonHighProbabilityRegretRate.lean:169
BanditRLProof.OFUL.telescopingCanonicalExplicitHighProbabilityPseudoRegretAllHorizonViolationSet_eq_standard theorem OFUL BanditRLProof.OFULScheduledAllHorizonHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledAllHorizonHighProbabilityRegretRate.lean:189
BanditRLProof.OFUL.telescopingCanonicalStandardHighProbabilityPseudoRegret_nonneg_and_allHorizon_tail_le_explicitBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledAllHorizonHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledAllHorizonHighProbabilityRegretRate.lean:225
BanditRLProof.OFUL.finiteHistoryScheduledScalarRidgeRadius definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:27
BanditRLProof.OFUL.finiteHistoryScheduledScalarRidgeOptimisticScore definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:37
BanditRLProof.OFUL.finiteHistoryScheduledScalarRidgeOptimisticScore_eq theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:53
BanditRLProof.OFUL.measurable_finiteHistoryScheduledScalarRidgeOptimisticScore theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:67
BanditRLProof.OFUL.finiteHistoryScheduledScalarRidgeOptimisticAction definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:83
BanditRLProof.OFUL.finiteHistoryScheduledScalarRidgeOptimisticAction_eq theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:101
BanditRLProof.OFUL.finiteHistoryScheduledScalarRidgeOptimisticAction_score_max theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:115
BanditRLProof.OFUL.finiteHistoryScheduledScalarRidgeOptimisticAlgorithm definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:140
BanditRLProof.OFUL.finiteHistoryTelescopingScalarRidgeOptimisticAlgorithm definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:159
BanditRLProof.OFUL.finiteHistoryTelescopingScalarRidgeOptimisticAlgorithm_initialAction theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:171
BanditRLProof.OFUL.finiteHistoryScheduledScalarRidge_historyStepKernel_map_snd theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:186
BanditRLProof.OFUL.finiteHistoryScheduledScalarRidgeSelectedFeature definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:229
BanditRLProof.OFUL.canonicalHistoryTrajectory_observedFeature_succ_ae_eq_scheduledSelectedFeature theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:243
BanditRLProof.OFUL.measurable_finiteHistoryScheduledScalarRidgeOptimisticAction theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:282
BanditRLProof.OFUL.scheduledCanonicalHistoryTrajectoryPredictableFeature definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:307
BanditRLProof.OFUL.scheduledCanonicalHistoryTrajectoryPredictableFeature_stronglyMeasurable theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:323
BanditRLProof.OFUL.scheduledCanonicalHistoryTrajectory_action_zero_ae_eq_initialArm theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:367
BanditRLProof.OFUL.canonicalHistoryTrajectoryFeature_ae_eq_scheduledPredictableFeature theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:419
BanditRLProof.OFUL.canonicalHistoryTrajectoryFeature_ae_eq_scheduledPredictableFeature_all theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:455
BanditRLProof.OFUL.scheduledCanonicalHistoryTrajectoryPredictableResidual definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:479
BanditRLProof.OFUL.scheduledCanonicalHistoryTrajectoryPredictableResidual_stronglyAdapted theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:494
BanditRLProof.OFUL.scheduledPredictableFeature_projection_le_finiteActionProjectionBound theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:554
BanditRLProof.OFUL.CanonicalScheduledPredictableScalarRidgeResidualLaw structure OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:597
BanditRLProof.OFUL.canonicalScheduledPredictableScalarRidgeResidualLaw_of_linearSubgaussianEnvironment definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:624
BanditRLProof.OFUL.mem_allTimeTelescopingScalarRidgeConfidenceFailureSet_iff_of_feature_eq theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:832
BanditRLProof.OFUL.measure_telescopingCanonicalHistoryTrajectory_allTimeConfidenceFailureSet_le theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:868
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectory_action_succ_ae_eq_scheduledAction theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:980
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectory_action_succ_gap_le_of_not_mem_confidenceFailure theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:1020
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectoryAllTimeSuccGapViolationSet definition OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:1115
BanditRLProof.OFUL.telescopingCanonicalHistoryTrajectoryAllTimeSuccGapViolationSet_subset_confidenceFailure_ae theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:1144
BanditRLProof.OFUL.measure_telescopingCanonicalHistoryTrajectoryAllTimeSuccGapViolationSet_le theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:1229
BanditRLProof.OFUL.measure_telescopingCanonicalHistoryTrajectory_allTimeConfidenceFailureSet_le_of_linearSubgaussianEnvironment theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:1279
BanditRLProof.OFUL.measure_telescopingCanonicalHistoryTrajectoryAllTimeSuccGapViolationSet_le_of_linearSubgaussianEnvironment theorem OFUL BanditRLProof.OFULScheduledAllTimeConfidence Compiled BanditRLProof/OFULScheduledAllTimeConfidence.lean:1313
BanditRLProof.OFUL.blockStartForcedIndexSet definition OFUL BanditRLProof.OFULScheduledBlockStartForcedActionChargeBound Compiled BanditRLProof/OFULScheduledBlockStartForcedActionChargeBound.lean:11
BanditRLProof.OFUL.card_blockStartForcedIndexSet_le_div_add_one theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedActionChargeBound Compiled BanditRLProof/OFULScheduledBlockStartForcedActionChargeBound.lean:20
BanditRLProof.OFUL.blockStartForcedActionSuccessorPseudoRegret_le_card_mul theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedActionChargeBound Compiled BanditRLProof/OFULScheduledBlockStartForcedActionChargeBound.lean:45
BanditRLProof.OFUL.blockStartForcedActionSuccessorPseudoRegret_le_div_add_one_mul theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedActionChargeBound Compiled BanditRLProof/OFULScheduledBlockStartForcedActionChargeBound.lean:77
BanditRLProof.OFUL.blockStartForcedActionSuccessorPseudoRegret_le_div_add_one_mul_two_mul_parameterFeatureBound theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedActionChargeBound Compiled BanditRLProof/OFULScheduledBlockStartForcedActionChargeBound.lean:111
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegretScalarAllHorizonViolationSet definition OFUL BanditRLProof.OFULScheduledBlockStartForcedActionChargeBound Compiled BanditRLProof/OFULScheduledBlockStartForcedActionChargeBound.lean:142
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegretScalarAllHorizonViolationSet_subset theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedActionChargeBound Compiled BanditRLProof/OFULScheduledBlockStartForcedActionChargeBound.lean:162
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegret_nonneg_and_scalarAllHorizon_tail_le_explicitBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedActionChargeBound Compiled BanditRLProof/OFULScheduledBlockStartForcedActionChargeBound.lean:198
BanditRLProof.OFUL.deterministicHistoryCanonicalPredictableFeature definition OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:23
BanditRLProof.OFUL.deterministicHistoryCanonicalPredictableFeature_stronglyMeasurable theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:37
BanditRLProof.OFUL.deterministicHistoryCanonical_action_zero_ae_eq_initialArm theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:73
BanditRLProof.OFUL.canonicalHistoryTrajectoryFeature_ae_eq_deterministicHistoryPredictableFeature theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:121
BanditRLProof.OFUL.canonicalHistoryTrajectoryFeature_ae_eq_deterministicHistoryPredictableFeature_all theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:159
BanditRLProof.OFUL.deterministicHistoryCanonicalPredictableResidual definition OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:184
BanditRLProof.OFUL.deterministicHistoryCanonicalPredictableResidual_stronglyAdapted theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:199
BanditRLProof.OFUL.deterministicHistoryPredictableFeature_projection_le_finiteActionProjectionBound theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:258
BanditRLProof.OFUL.deterministicHistory_historyStepKernel_map_snd theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:293
BanditRLProof.OFUL.CanonicalDeterministicHistoryPredictableScalarRidgeResidualLaw structure OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:320
BanditRLProof.OFUL.canonicalDeterministicHistoryPredictableScalarRidgeResidualLaw_of_linearSubgaussianEnvironment definition OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:348
BanditRLProof.OFUL.measure_deterministicHistoryCanonical_allTimeTelescopingScalarRidgeConfidenceFailureSet_le theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:545
BanditRLProof.OFUL.canonicalBlockStartForcedPredictableScalarRidgeResidualLaw_of_linearSubgaussianEnvironment definition OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:658
BanditRLProof.OFUL.measure_blockStartForcedCanonicalHistoryTrajectory_allTimeConfidenceFailureSet_le theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:688
BanditRLProof.OFUL.measure_blockStartForcedCanonicalHistoryTrajectory_allTimeConfidenceFailureSet_le_of_linearSubgaussianEnvironment theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:733
BanditRLProof.OFUL.blockStartOptimisticSuccessorRadiusWidthCharge_le_telescopingStandardScalarRadiusWidthBound theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:767
BanditRLProof.OFUL.blockStartForcedCanonicalHistoryTrajectory_initialGap_le_ae theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:844
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegret_le_forcedActionCharge_add_explicitBound_ae theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:891
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegretAllHorizonViolationSet definition OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:952
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegretAllHorizonViolationSet_subset_confidenceFailure_ae theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:973
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegret_nonneg_and_allHorizon_tail_le_explicitBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledBlockStartForcedAllTimeConfidence.lean:1022
BanditRLProof.Thompson.deterministicHistoryAlgorithm definition OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:28
BanditRLProof.Thompson.deterministicHistoryAlgorithm_policy_apply theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:41
BanditRLProof.Thompson.canonicalHistoryTrajectory_action_succ_ae_eq_deterministicHistorySelector theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:59
BanditRLProof.OFUL.finiteHistoryBlockStartForcedTelescopingScalarRidgeAction definition OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:140
BanditRLProof.OFUL.measurable_finiteHistoryBlockStartForcedTelescopingScalarRidgeAction theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:158
BanditRLProof.OFUL.finiteHistoryBlockStartForcedTelescopingScalarRidgeAlgorithm definition OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:181
BanditRLProof.OFUL.finiteHistoryBlockStartForcedTelescopingScalarRidgeAlgorithm_policy_apply theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:200
BanditRLProof.OFUL.finiteHistoryBlockStartForcedTelescopingScalarRidgeAction_mul_window theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:226
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_succ_ae_eq_finiteHistoryBlockStartForcedTelescopingScalarRidgeAction theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:248
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_blockStart_succ_ae_eq_forcedAction theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:283
BanditRLProof.Budget.alignedWindowPositiveActionCostAE_finiteHistoryBlockStartForcedTelescopingScalarRidgeAlgorithm theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledBlockStartForcedHistoryAlgorithm.lean:320
BanditRLProof.OFUL.blockStartForcedHorizonIndexedCanonicalTrajectoryMeasure definition OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate.lean:14
BanditRLProof.OFUL.blockStartForcedHorizonIndexedCanonicalTrajectoryMeasure_apply theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate.lean:32
BanditRLProof.OFUL.blockStartForcedHorizonIndexedCanonicalStandardHighProbabilityPseudoRegretViolationSet definition OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate.lean:53
BanditRLProof.OFUL.blockStartForcedHorizonIndexedCanonicalStandardHighProbabilityPseudoRegretViolationSet_apply theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate.lean:68
BanditRLProof.OFUL.blockStartForcedHorizonIndexedCanonicalStandardHighProbabilityPseudoRegret_nonneg_and_tail_le_explicitBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonIndexedHighProbabilityRegretRate.lean:88
BanditRLProof.OFUL.blockStartForcedIndexSet_horizon_self_eq_singleton theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail.lean:11
BanditRLProof.OFUL.blockStartForcedActionSuccessorPseudoRegret_horizon_self theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail.lean:29
BanditRLProof.OFUL.blockStartForcedActionSuccessorPseudoRegret_horizon_self_le_two_mul_parameterFeatureBound theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail.lean:53
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegretHorizonWindowViolationSet definition OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail.lean:80
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegretHorizonWindowViolationSet_subset theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail.lean:102
BanditRLProof.OFUL.blockStartForcedCanonicalStandardHighProbabilityPseudoRegret_horizonWindow_nonneg_and_finiteHorizon_tail_le_explicitBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail Compiled BanditRLProof/OFULScheduledBlockStartForcedHorizonWindowFiniteHorizonTail.lean:137
BanditRLProof.OFUL.finiteHistoryTelescopingScalarRidgeOptimisticAction definition OFUL BanditRLProof.OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret.lean:32
BanditRLProof.OFUL.finiteHistoryTelescopingScalarRidgeOptimisticAlgorithm_policy_apply theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret.lean:46
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_succ_ae_eq_finiteHistoryTelescopingScalarRidgeOptimisticAction theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret.lean:71
BanditRLProof.Budget.alignedWindowPositiveActionCostAE_of_blockStartTelescopingActionCostPositive theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret.lean:111
BanditRLProof.Budget.alignedWindowPositiveActionCostAE_of_blockStartForcedTelescopingAction theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret.lean:153
BanditRLProof.Budget.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_budgetWindowRoundsSq_add_initialGap_mul_budgetWindowRounds_mul_sqrt_delta_and_stoppedViolation_measure_le_of_blockStartForcedPositiveActionCostBudgetExhaustionTime theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBlockStartForcedPositiveActionCostBudgetExhaustionExpectedRegret.lean:194
BanditRLProof.OFUL.finiteHistoryBlockStartForcedTelescopingScalarRidgeAction_eq_of_mod_ne_zero theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:22
BanditRLProof.OFUL.finiteHistoryBlockStartForcedTelescopingScalarRidgeAction_eq_forcedAction_of_mod_eq_zero theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:41
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_succ_ae_eq_finiteHistoryTelescopingScalarRidgeOptimisticAction_of_mod_ne_zero theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:62
BanditRLProof.OFUL.blockStartForcedSuccessorPseudoRegret definition OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:95
BanditRLProof.OFUL.blockStartForcedActionSuccessorPseudoRegret definition OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:110
BanditRLProof.OFUL.blockStartOptimisticSuccessorPseudoRegret definition OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:123
BanditRLProof.OFUL.blockStartOptimisticSuccessorRadiusWidthCharge definition OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:138
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_succ_gap_le_of_eq_telescopingAction_of_not_mem_confidenceFailure theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:163
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret_eq_initial_add_blockStartForced_add_optimistic theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:259
BanditRLProof.OFUL.blockStartForcedSuccessorPseudoRegret_ae_eq_forcedActionCharge theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:290
BanditRLProof.OFUL.blockStartOptimisticSuccessorPseudoRegret_le_radiusWidthCharge_ae_of_not_mem_allTimeConfidenceFailure theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:358
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret_le_initial_add_blockStartForced_add_radiusWidthCharge_ae_of_not_mem_allTimeConfidenceFailure theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:440
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret_le_initial_add_forcedActionCharge_add_radiusWidthCharge_ae_of_not_mem_allTimeConfidenceFailure theorem OFUL BanditRLProof.OFULScheduledBlockStartForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledBlockStartForcedPseudoRegretDecomposition.lean:488
BanditRLProof.OFUL.telescopingHighProbabilityRegretLogBudget_nonneg theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegret.lean:23
BanditRLProof.OFUL.telescopingHighProbabilityRegretLogBudget_mono theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegret.lean:59
BanditRLProof.OFUL.telescopingHighProbabilityPseudoRegretBound_nonneg theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegret.lean:110
BanditRLProof.OFUL.telescopingHighProbabilityPseudoRegretBound_mono theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegret.lean:127
BanditRLProof.OFUL.standardScalarAllRoundGapEnvelope_mono theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegret.lean:206
BanditRLProof.OFUL.abs_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_le_envelope theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegret.lean:222
BanditRLProof.OFUL.integrable_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_of_boundedStoppingTime theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegret.lean:268
BanditRLProof.OFUL.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_le_endpoint_add_envelope_mul_real_measure theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegret.lean:325
BanditRLProof.OFUL.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_endpoint_add_envelope_mul_delta_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegret.lean:491
BanditRLProof.OFUL.telescopingStandardExpectedConfidenceLog_isBigO_log_succ theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretAsymptotics Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretAsymptotics.lean:23
BanditRLProof.OFUL.telescopingStandardExpectedRegretLogBudget_isBigO_log theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretAsymptotics Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretAsymptotics.lean:81
BanditRLProof.OFUL.telescopingStandardExpectedPseudoRegretBound_isBigO_sqrt_mul_log theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretAsymptotics Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretAsymptotics.lean:101
BanditRLProof.OFUL.canonicalTelescopingStandardExpectedStoppedPseudoRegret_isBigO_sqrt_mul_log theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretAsymptotics Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretAsymptotics.lean:229
BanditRLProof.OFUL.telescopingStandardExpectedPseudoRegretBound_isLittleO_natCast_succ theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretConsistency Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretConsistency.lean:23
BanditRLProof.OFUL.canonicalTelescopingStandardExpectedStoppedPseudoRegret_isLittleO_natCast_succ theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretConsistency Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretConsistency.lean:41
BanditRLProof.OFUL.canonicalTelescopingStandardExpectedAverageStoppedPseudoRegret definition OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretConsistency Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretConsistency.lean:80
BanditRLProof.OFUL.canonicalTelescopingStandardExpectedAverageStoppedPseudoRegret_tendsto_zero theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretConsistency Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretConsistency.lean:101
BanditRLProof.OFUL.telescopingStandardExpectedRegretLogBudget definition OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretRate.lean:24
BanditRLProof.OFUL.telescopingHighProbabilityRegretLogBudget_standardExpectedRegretDelta theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretRate.lean:37
BanditRLProof.OFUL.telescopingStandardExpectedPseudoRegretBound definition OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretRate.lean:62
BanditRLProof.OFUL.telescopingHighProbabilityPseudoRegretBound_add_initial_standardExpectedRegretDelta_eq theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretRate.lean:81
BanditRLProof.OFUL.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_telescopingStandardExpectedBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretRate.lean:104
BanditRLProof.OFUL.canonicalTelescopingStandardExpectedStoppedPseudoRegret definition OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretRate.lean:164
BanditRLProof.OFUL.canonicalTelescopingStandardExpectedStoppedPseudoRegret_nonneg_and_le theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeExpectedRegretRate.lean:192
BanditRLProof.OFUL.canonicalHistoryTrajectoryAllRoundFiltration definition OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:24
BanditRLProof.OFUL.canonicalHistoryTrajectoryAllRoundFiltration_apply theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:31
BanditRLProof.OFUL.measurable_canonicalHistoryTrajectory_coordinate_allRound theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:39
BanditRLProof.OFUL.boundedTrajectoryTime_ne_top theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:63
BanditRLProof.OFUL.coe_untopA_boundedTrajectoryTime theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:75
BanditRLProof.OFUL.measurable_canonicalStandardHighProbabilityPseudoRegret_allRound theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:92
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret_stronglyAdapted_allRound theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:150
BanditRLProof.OFUL.telescopingHighProbabilityPseudoRegretBound_stronglyAdapted_allRound theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:168
BanditRLProof.OFUL.telescopingCanonicalExplicitHighProbabilityPseudoRegretStoppedViolationSet definition OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:185
BanditRLProof.OFUL.telescopingCanonicalExplicitHighProbabilityPseudoRegretStoppedViolationSet_subset_allHorizon theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:212
BanditRLProof.OFUL.measurableSet_telescopingCanonicalExplicitHighProbabilityPseudoRegretStoppedViolationSet_of_boundedStoppingTime theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:236
BanditRLProof.OFUL.measure_telescopingCanonicalExplicitHighProbabilityPseudoRegretStoppedViolationSet_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:297
BanditRLProof.OFUL.telescopingCanonicalStandardHighProbabilityPseudoRegret_nonneg_and_boundedStoppingTime_tail_le_explicitBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledBoundedStoppingTimeHighProbabilityRegretRate.lean:351
BanditRLProof.OFUL.squareIntegrableFiniteStoppingTime_of_bounded theorem OFUL BanditRLProof.OFULScheduledBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBudgetExhaustionExpectedRegret.lean:26
BanditRLProof.OFUL.stoppingTimeRoundSecondMoment_le_sq_of_bounded theorem OFUL BanditRLProof.OFULScheduledBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBudgetExhaustionExpectedRegret.lean:57
BanditRLProof.Budget.budgetExhaustionTime_le_budget_of_spent_budget theorem OFUL BanditRLProof.OFULScheduledBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBudgetExhaustionExpectedRegret.lean:104
BanditRLProof.Budget.squareIntegrableFiniteStoppingTime_budgetExhaustionTime theorem OFUL BanditRLProof.OFULScheduledBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBudgetExhaustionExpectedRegret.lean:121
BanditRLProof.Budget.stoppingTimeRoundSecondMoment_budgetExhaustionTime_le theorem OFUL BanditRLProof.OFULScheduledBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBudgetExhaustionExpectedRegret.lean:143
BanditRLProof.Budget.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_budgetRoundsSq_add_initialGap_mul_budgetRounds_mul_sqrt_delta_and_stoppedViolation_measure_le_of_budgetExhaustionTime theorem OFUL BanditRLProof.OFULScheduledBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledBudgetExhaustionExpectedRegret.lean:171
BanditRLProof.Budget.budgetExhaustionTime_le_reachHorizon_of_spent_reach theorem OFUL BanditRLProof.OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret.lean:24
BanditRLProof.Budget.squareIntegrableFiniteStoppingTime_budgetExhaustionTime_of_reachHorizon theorem OFUL BanditRLProof.OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret.lean:42
BanditRLProof.Budget.stoppingTimeRoundSecondMoment_budgetExhaustionTime_le_of_reachHorizon theorem OFUL BanditRLProof.OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret.lean:64
BanditRLProof.Budget.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_reachHorizonRoundsSq_add_initialGap_mul_reachHorizonRounds_mul_sqrt_delta_and_stoppedViolation_measure_le_of_budgetExhaustionTime_reachedBy theorem OFUL BanditRLProof.OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret.lean:93
BanditRLProof.Budget.block_le_cumulativeSpent_mul_of_alignedWindowPositive theorem OFUL BanditRLProof.OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret.lean:187
BanditRLProof.Budget.budget_le_cumulativeSpent_budget_mul_of_alignedWindowPositive theorem OFUL BanditRLProof.OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret.lean:235
BanditRLProof.Budget.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_budgetWindowRoundsSq_add_initialGap_mul_budgetWindowRounds_mul_sqrt_delta_and_stoppedViolation_measure_le_of_cumulativeAlignedWindowPositiveCostBudgetExhaustionTime theorem OFUL BanditRLProof.OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativeAlignedWindowPositiveCostBudgetExhaustionExpectedRegret.lean:253
BanditRLProof.Budget.cumulativeSpent definition OFUL BanditRLProof.OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret.lean:24
BanditRLProof.Budget.cumulativeSpent_zero theorem OFUL BanditRLProof.OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret.lean:32
BanditRLProof.Budget.cumulativeSpent_succ theorem OFUL BanditRLProof.OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret.lean:40
BanditRLProof.Budget.adapted_cumulativeSpent theorem OFUL BanditRLProof.OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret.lean:53
BanditRLProof.Budget.cumulativeSpent_unitGrowth_of_one_le theorem OFUL BanditRLProof.OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret.lean:69
BanditRLProof.Budget.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_budgetRoundsSq_add_initialGap_mul_budgetRounds_mul_sqrt_delta_and_stoppedViolation_measure_le_of_cumulativePositiveCostBudgetExhaustionTime theorem OFUL BanditRLProof.OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledCumulativePositiveCostBudgetExhaustionExpectedRegret.lean:85
BanditRLProof.Budget.canonicalActionCostProcess definition OFUL BanditRLProof.OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret.lean:21
BanditRLProof.Budget.adapted_canonicalActionCostProcess theorem OFUL BanditRLProof.OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret.lean:33
BanditRLProof.Budget.canonicalActionCostProcess_one_le theorem OFUL BanditRLProof.OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret.lean:47
BanditRLProof.Budget.cumulativeActionCost definition OFUL BanditRLProof.OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret.lean:59
BanditRLProof.Budget.cumulativeActionCost_apply theorem OFUL BanditRLProof.OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret.lean:67
BanditRLProof.Budget.adapted_cumulativeActionCost theorem OFUL BanditRLProof.OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret.lean:77
BanditRLProof.Budget.cumulativeActionCost_unitGrowth_of_one_le theorem OFUL BanditRLProof.OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret.lean:88
BanditRLProof.Budget.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_budgetRoundsSq_add_initialGap_mul_budgetRounds_mul_sqrt_delta_and_stoppedViolation_measure_le_of_positiveActionCostBudgetExhaustionTime theorem OFUL BanditRLProof.OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledPositiveActionCostBudgetExhaustionExpectedRegret.lean:104
BanditRLProof.OFUL.powerOfTwoOptimisticSuccessorRadiusWidthCharge definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:24
BanditRLProof.OFUL.powerOfTwoOptimisticSuccessorPseudoRegret_le_radiusWidthCharge_ae_of_not_mem_allTimeConfidenceFailure theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:50
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret_le_initial_add_powerOfTwoForced_add_radiusWidthCharge_ae_of_not_mem_allTimeConfidenceFailure theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:132
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret_le_initial_add_powerOfTwoForcedActionCharge_add_radiusWidthCharge_ae_of_not_mem_allTimeConfidenceFailure theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:180
BanditRLProof.OFUL.canonicalPowerOfTwoForcedPredictableScalarRidgeResidualLaw_of_linearSubgaussianEnvironment definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:224
BanditRLProof.OFUL.measure_powerOfTwoForcedCanonicalHistoryTrajectory_allTimeConfidenceFailureSet_le theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:253
BanditRLProof.OFUL.measure_powerOfTwoForcedCanonicalHistoryTrajectory_allTimeConfidenceFailureSet_le_of_linearSubgaussianEnvironment theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:293
BanditRLProof.OFUL.powerOfTwoOptimisticSuccessorRadiusWidthCharge_le_telescopingStandardScalarRadiusWidthBound theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:326
BanditRLProof.OFUL.powerOfTwoForcedCanonicalHistoryTrajectory_initialGap_le_ae theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:404
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityPseudoRegret_le_forcedActionCharge_add_explicitBound_ae theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:449
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityPseudoRegretAllHorizonViolationSet definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:509
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityPseudoRegretAllHorizonViolationSet_subset_confidenceFailure_ae theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:529
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityPseudoRegret_nonneg_and_allHorizon_tail_le_explicitBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedAllTimeConfidence Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedAllTimeConfidence.lean:575
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityAveragePseudoRegret_tendsto_zero_of_not_mem_allHorizonViolationSet theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageConsistency Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageConsistency.lean:23
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityAveragePseudoRegretConsistencyFailureSet definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageConsistency Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageConsistency.lean:66
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityAveragePseudoRegretConsistencyFailureSet_subset_allHorizonViolationSet theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageConsistency Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageConsistency.lean:84
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityAveragePseudoRegret_tendsto_zero_off_violation_and_consistencyFailure_tail_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageConsistency Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageConsistency.lean:119
BanditRLProof.OFUL.powerOfTwoForcedScalarHighProbabilityPseudoRegretBound_isLittleO_natCast_succ theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret.lean:23
BanditRLProof.OFUL.powerOfTwoForcedScalarHighProbabilityAveragePseudoRegretBound definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret.lean:40
BanditRLProof.OFUL.powerOfTwoForcedScalarHighProbabilityAveragePseudoRegretBound_tendsto_zero theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret.lean:48
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityAveragePseudoRegret definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret.lean:66
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityAveragePseudoRegret_le_averageBound_of_not_mem_allHorizonViolationSet theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret.lean:83
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityPseudoRegret_averageBudget_tendsto_zero_nonneg_and_allHorizon_tail_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityAverageRegret.lean:122
BanditRLProof.OFUL.powerOfTwoForcedScalarHighProbabilityPseudoRegretBound definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate.lean:22
BanditRLProof.OFUL.telescopingHighProbabilityRegretLogBudget_anti_delta theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate.lean:34
BanditRLProof.OFUL.telescopingHighProbabilityRegretLogBudget_isBigO_log_succ theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate.lean:78
BanditRLProof.OFUL.telescopingHighProbabilityPseudoRegretBound_isBigO_sqrt_mul_log theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate.lean:194
BanditRLProof.OFUL.natCast_log2_add_one_isBigO_log_succ theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate.lean:321
BanditRLProof.OFUL.powerOfTwoForcedScalarHighProbabilityPseudoRegretBound_isBigO_sqrt_mul_log theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate.lean:393
BanditRLProof.OFUL.powerOfTwoForcedCanonicalAsymptoticHighProbabilityPseudoRegretAllHorizonViolationSet definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate.lean:455
BanditRLProof.OFUL.powerOfTwoForcedCanonicalAsymptoticHighProbabilityPseudoRegretAllHorizonViolationSet_eq_scalar theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate.lean:472
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityPseudoRegret_asymptoticRate_nonneg_and_allHorizon_tail_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHighProbabilityRegretRate.lean:493
BanditRLProof.OFUL.finiteHistoryPowerOfTwoForcedTelescopingScalarRidgeAction definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHistoryAlgorithm.lean:26
BanditRLProof.OFUL.measurable_finiteHistoryPowerOfTwoForcedTelescopingScalarRidgeAction theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHistoryAlgorithm.lean:44
BanditRLProof.OFUL.finiteHistoryPowerOfTwoForcedTelescopingScalarRidgeAlgorithm definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHistoryAlgorithm.lean:67
BanditRLProof.OFUL.finiteHistoryPowerOfTwoForcedTelescopingScalarRidgeAlgorithm_policy_apply theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHistoryAlgorithm.lean:85
BanditRLProof.OFUL.finiteHistoryPowerOfTwoForcedTelescopingScalarRidgeAction_pow_sub_one theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHistoryAlgorithm.lean:114
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_succ_ae_eq_finiteHistoryPowerOfTwoForcedTelescopingScalarRidgeAction theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHistoryAlgorithm.lean:138
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_pow_ae_eq_forcedAction theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedHistoryAlgorithm Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedHistoryAlgorithm.lean:172
BanditRLProof.OFUL.isPowerOfTwoForcedIndex definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedIndexCount Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedIndexCount.lean:12
BanditRLProof.OFUL.isPowerOfTwoForcedIndex_iff theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedIndexCount Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedIndexCount.lean:21
BanditRLProof.OFUL.powerOfTwoForcedIndexSet definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedIndexCount Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedIndexCount.lean:31
BanditRLProof.OFUL.mem_powerOfTwoForcedIndexSet_iff theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedIndexCount Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedIndexCount.lean:35
BanditRLProof.OFUL.powerOfTwoForcedIndexSet_zero theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedIndexCount Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedIndexCount.lean:45
BanditRLProof.OFUL.zero_mem_powerOfTwoForcedIndexSet_iff theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedIndexCount Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedIndexCount.lean:51
BanditRLProof.OFUL.card_powerOfTwoForcedIndexSet_le_log2_add_one theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedIndexCount Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedIndexCount.lean:63
BanditRLProof.OFUL.finiteHistoryPowerOfTwoForcedTelescopingScalarRidgeAction_eq_of_not_forced theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:23
BanditRLProof.OFUL.finiteHistoryPowerOfTwoForcedTelescopingScalarRidgeAction_eq_forcedAction theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:44
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_succ_ae_eq_finiteHistoryTelescopingScalarRidgeOptimisticAction_of_not_powerOfTwoForced theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:67
BanditRLProof.OFUL.canonicalHistoryTrajectory_action_succ_ae_eq_forcedAction_of_powerOfTwoForced theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:99
BanditRLProof.OFUL.powerOfTwoForcedSuccessorPseudoRegret definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:129
BanditRLProof.OFUL.powerOfTwoForcedActionSuccessorPseudoRegret definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:144
BanditRLProof.OFUL.powerOfTwoOptimisticSuccessorPseudoRegret definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:158
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret_eq_initial_add_powerOfTwoForced_add_optimistic theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:177
BanditRLProof.OFUL.powerOfTwoForcedSuccessorPseudoRegret_ae_eq_forcedActionCharge theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:210
BanditRLProof.OFUL.canonicalStandardHighProbabilityPseudoRegret_ae_eq_initial_add_powerOfTwoForcedAction_add_optimistic theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedPseudoRegretDecomposition.lean:272
BanditRLProof.OFUL.powerOfTwoForcedActionSuccessorPseudoRegret_le_card_mul theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedScalarChargeBound Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedScalarChargeBound.lean:22
BanditRLProof.OFUL.powerOfTwoForcedActionSuccessorPseudoRegret_le_log2_add_one_mul theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedScalarChargeBound Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedScalarChargeBound.lean:54
BanditRLProof.OFUL.powerOfTwoForcedActionSuccessorPseudoRegret_le_log2_add_one_mul_two_mul_parameterFeatureBound theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedScalarChargeBound Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedScalarChargeBound.lean:86
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityPseudoRegretScalarAllHorizonViolationSet definition OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedScalarChargeBound Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedScalarChargeBound.lean:121
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityPseudoRegretScalarAllHorizonViolationSet_subset theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedScalarChargeBound Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedScalarChargeBound.lean:140
BanditRLProof.OFUL.powerOfTwoForcedCanonicalStandardHighProbabilityPseudoRegret_nonneg_and_scalarAllHorizon_tail_le_explicitBound_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledPowerOfTwoForcedScalarChargeBound Compiled BanditRLProof/OFULScheduledPowerOfTwoForcedScalarChargeBound.lean:173
BanditRLProof.OFUL.IntegrableFiniteStoppingTime structure OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegret.lean:26
BanditRLProof.OFUL.abs_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_le_randomHorizonEnvelope theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegret.lean:34
BanditRLProof.OFUL.measurable_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_of_stoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegret.lean:61
BanditRLProof.OFUL.measurable_stoppedValue_telescopingHighProbabilityPseudoRegretBound_of_stoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegret.lean:84
BanditRLProof.OFUL.integrable_standardScalarAllRoundGapEnvelope_at_stoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegret.lean:105
BanditRLProof.OFUL.integrable_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_of_integrableFiniteStoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegret.lean:122
BanditRLProof.OFUL.measurableSet_telescopingCanonicalExplicitHighProbabilityPseudoRegretStoppedViolationSet_of_stoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegret.lean:157
BanditRLProof.OFUL.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_le_integral_stoppedBudget_add_integral_badIndicator_randomHorizonEnvelope theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegret.lean:182
BanditRLProof.OFUL.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_integral_stoppedBudget_add_integral_badIndicator_randomHorizonEnvelope_and_stoppedViolation_measure_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegret Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegret.lean:303
BanditRLProof.OFUL.standardScalarLogDetBudget_le_rounds_mul_div theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretClosed Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretClosed.lean:20
BanditRLProof.OFUL.telescopingHighProbabilityPseudoRegretQuadraticCoefficient definition OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretClosed Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretClosed.lean:57
BanditRLProof.OFUL.telescopingHighProbabilityPseudoRegretQuadraticCoefficient_nonneg theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretClosed Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretClosed.lean:67
BanditRLProof.OFUL.telescopingHighProbabilityRegretLogBudget_le_rounds_sq_mul theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretClosed Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretClosed.lean:86
BanditRLProof.OFUL.telescopingHighProbabilityPseudoRegretBound_le_rounds_sq_mul_coefficient theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretClosed Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretClosed.lean:163
BanditRLProof.OFUL.integrable_stoppedValue_telescopingHighProbabilityPseudoRegretBound_of_squareIntegrableFiniteStoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretClosed Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretClosed.lean:320
BanditRLProof.OFUL.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_integral_stoppedBudget_add_initialGap_mul_sqrt_roundSecondMoment_mul_sqrt_delta_and_stoppedViolation_measure_le_of_squareIntegrableFiniteStoppingTime_automaticBudgetIntegrability theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretClosed Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretClosed.lean:371
BanditRLProof.OFUL.stoppingTimeRoundSecondMoment definition OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretExactMoment Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretExactMoment.lean:24
BanditRLProof.OFUL.stoppingTimeRoundSecondMoment_nonneg theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretExactMoment Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretExactMoment.lean:32
BanditRLProof.OFUL.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_stoppingTimeRoundSecondMoment_add_initialGap_mul_sqrt_stoppingTimeRoundSecondMoment_mul_sqrt_delta_and_stoppedViolation_measure_le_of_squareIntegrableFiniteStoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretExactMoment Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretExactMoment.lean:44
BanditRLProof.OFUL.SquareIntegrableFiniteStoppingTime structure OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretRate.lean:25
BanditRLProof.OFUL.SquareIntegrableFiniteStoppingTime.toIntegrableFiniteStoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretRate.lean:33
BanditRLProof.OFUL.integral_indicator_le_sqrt_secondMoment_mul_sqrt_real_measure theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretRate.lean:46
BanditRLProof.OFUL.integral_badIndicator_standardScalarAllRoundGapEnvelope_at_stoppingTime_le theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretRate.lean:98
BanditRLProof.OFUL.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_integral_stoppedBudget_add_initialGap_mul_sqrt_roundSecondMoment_mul_sqrt_delta_and_stoppedViolation_measure_le_of_linearSubgaussianEnvironment_of_featureBound_le_regularization theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretRate Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretRate.lean:174
BanditRLProof.OFUL.integral_stoppedValue_telescopingHighProbabilityPseudoRegretBound_le_quadraticCoefficient_mul_roundSecondMoment_of_squareIntegrableFiniteStoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretSecondMoment Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretSecondMoment.lean:23
BanditRLProof.OFUL.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_roundSecondMoment_add_initialGap_mul_sqrt_roundSecondMoment_mul_sqrt_delta_and_stoppedViolation_measure_le_of_squareIntegrableFiniteStoppingTime theorem OFUL BanditRLProof.OFULScheduledUnboundedStoppingTimeExpectedRegretSecondMoment Compiled BanditRLProof/OFULScheduledUnboundedStoppingTimeExpectedRegretSecondMoment.lean:114
BanditRLProof.Budget.index_le_spent_of_unitGrowth theorem OFUL BanditRLProof.OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret.lean:24
BanditRLProof.Budget.budgetExhaustionTime_le_budget_of_unitGrowth theorem OFUL BanditRLProof.OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret.lean:43
BanditRLProof.Budget.squareIntegrableFiniteStoppingTime_budgetExhaustionTime_of_unitGrowth theorem OFUL BanditRLProof.OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret.lean:59
BanditRLProof.Budget.stoppingTimeRoundSecondMoment_budgetExhaustionTime_le_of_unitGrowth theorem OFUL BanditRLProof.OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret.lean:79
BanditRLProof.Budget.integral_stoppedValue_canonicalStandardHighProbabilityPseudoRegret_nonneg_and_le_quadraticCoefficient_mul_budgetRoundsSq_add_initialGap_mul_budgetRounds_mul_sqrt_delta_and_stoppedViolation_measure_le_of_budgetExhaustionTime_of_unitGrowth theorem OFUL BanditRLProof.OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret Compiled BanditRLProof/OFULScheduledUnitGrowthBudgetExhaustionExpectedRegret.lean:105
BanditRLProof.OFUL.clippedConfidenceWidth definition OFUL BanditRLProof.OFULSelectedWidthSummation Compiled BanditRLProof/OFULSelectedWidthSummation.lean:21
BanditRLProof.OFUL.clippedConfidenceWidth_eq_min_one_confidenceWidth theorem OFUL BanditRLProof.OFULSelectedWidthSummation Compiled BanditRLProof/OFULSelectedWidthSummation.lean:27
BanditRLProof.OFUL.sum_range_clippedConfidenceWidth_le_sqrt_mul_sqrt_log theorem OFUL BanditRLProof.OFULSelectedWidthSummation Compiled BanditRLProof/OFULSelectedWidthSummation.lean:46
BanditRLProof.OFUL.sum_range_min_one_confidenceWidth_le_sqrt_mul_sqrt_log theorem OFUL BanditRLProof.OFULSelectedWidthSummation Compiled BanditRLProof/OFULSelectedWidthSummation.lean:112
BanditRLProof.OFUL.sum_range_confidenceWidth_le_sqrt_mul_sqrt_log_of_width_le_one theorem OFUL BanditRLProof.OFULSelectedWidthSummation Compiled BanditRLProof/OFULSelectedWidthSummation.lean:155
BanditRLProof.OFUL.sum_range_selectedAction_min_one_confidenceWidth_le_sqrt_mul_sqrt_log theorem OFUL BanditRLProof.OFULSelectedWidthSummation Compiled BanditRLProof/OFULSelectedWidthSummation.lean:194
BanditRLProof.OFUL.sum_range_selectedAction_confidenceWidth_le_sqrt_mul_sqrt_log_of_width_le_one theorem OFUL BanditRLProof.OFULSelectedWidthSummation Compiled BanditRLProof/OFULSelectedWidthSummation.lean:222
ProbabilityTheory.HasCondSubgaussianMGF.predictable_mul_compensated_hasCondMGFUpperBoundAt theorem OFUL BanditRLProof.OFULSelfNormalizedConfidence Compiled BanditRLProof/OFULSelfNormalizedConfidence.lean:31
ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul_predictable_mul_compensated_of_abs_le theorem OFUL BanditRLProof.OFULSelfNormalizedConfidence Compiled BanditRLProof/OFULSelfNormalizedConfidence.lean:134
ProbabilityTheory.HasCondSubgaussianMGF.predictable_mul_compensated_hasCondMGFUpperBoundAt_of_abs_le theorem OFUL BanditRLProof.OFULSelfNormalizedConfidence Compiled BanditRLProof/OFULSelfNormalizedConfidence.lean:221
BanditRLProof.OFUL.fixedDirectionCompensatedScore_hasMGFUpperBoundAt theorem OFUL BanditRLProof.OFULSelfNormalizedConfidence Compiled BanditRLProof/OFULSelfNormalizedConfidence.lean:259
BanditRLProof.OFUL.constantSquaredVarianceProxy definition OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:20
BanditRLProof.OFUL.finiteHorizonFeatureGram definition OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:24
BanditRLProof.OFUL.finiteHorizonVarianceGram_constantSquared_eq_smul_featureGram theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:33
BanditRLProof.OFUL.finiteHorizonFeatureGram_posSemidef theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:51
BanditRLProof.OFUL.sq_smul_posDef theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:64
BanditRLProof.OFUL.det_sq_smul_div_det_sq_smul theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:77
BanditRLProof.OFUL.dotProduct_sq_smul_inv_mulVec theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:91
BanditRLProof.OFUL.measure_inv_le_finiteHorizonDetRatioInvGramExponential_le theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:109
BanditRLProof.OFUL.measure_invOfReal_le_finiteHorizonDetRatioInvGramExponential_le theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:182
BanditRLProof.OFUL.invOfReal_le_gaussianDetRatioExponential_of_invGramQuadratic_gt theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:225
BanditRLProof.OFUL.measure_finiteHorizon_invGramQuadratic_gt_two_log_detRatio_div_le theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:296
BanditRLProof.OFUL.measure_finiteHorizon_selfNormalizedQuadratic_gt_two_mul_sq_mul_log_detRatio_div_le theorem OFUL BanditRLProof.OFULSelfNormalizedMarkov Compiled BanditRLProof/OFULSelfNormalizedMarkov.lean:380
BanditRLProof.OFUL.scalarRidgeConfidenceFailureAt definition OFUL BanditRLProof.OFULUniformTimeConfidence Compiled BanditRLProof/OFULUniformTimeConfidence.lean:23
BanditRLProof.OFUL.finiteHorizonScheduledScalarRidgeConfidenceFailureSet definition OFUL BanditRLProof.OFULUniformTimeConfidence Compiled BanditRLProof/OFULUniformTimeConfidence.lean:47
BanditRLProof.OFUL.mem_finiteHorizonScheduledScalarRidgeConfidenceFailureSet_iff theorem OFUL BanditRLProof.OFULUniformTimeConfidence Compiled BanditRLProof/OFULUniformTimeConfidence.lean:63
BanditRLProof.OFUL.not_mem_finiteHorizonScheduledScalarRidgeConfidenceFailureSet_iff theorem OFUL BanditRLProof.OFULUniformTimeConfidence Compiled BanditRLProof/OFULUniformTimeConfidence.lean:86
BanditRLProof.OFUL.measure_finiteHorizonScheduledScalarRidgeConfidenceFailureSet_le_sum theorem OFUL BanditRLProof.OFULUniformTimeConfidence Compiled BanditRLProof/OFULUniformTimeConfidence.lean:116
BanditRLProof.OFUL.finiteHorizonUniformScalarRidgeConfidenceFailureSet definition OFUL BanditRLProof.OFULUniformTimeConfidence Compiled BanditRLProof/OFULUniformTimeConfidence.lean:188
BanditRLProof.OFUL.measure_finiteHorizonUniformScalarRidgeConfidenceFailureSet_le theorem OFUL BanditRLProof.OFULUniformTimeConfidence Compiled BanditRLProof/OFULUniformTimeConfidence.lean:206
BanditRLProof.ProblemArea inductive type Frontier BanditRLProof.OpenProblems Compiled BanditRLProof/OpenProblems.lean:9
BanditRLProof.OpenProblem structure Frontier BanditRLProof.OpenProblems Compiled BanditRLProof/OpenProblems.lean:19
BanditRLProof.seedOpenProblems definition Frontier BanditRLProof.OpenProblems Compiled BanditRLProof/OpenProblems.lean:28
BanditRLProof.Policy.MeasurablePolicy structure Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:21
BanditRLProof.Policy.measurable_action_of_measurable_state theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:29
BanditRLProof.Policy.measurable_action_mem_filtration_of_measurable_state theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:43
BanditRLProof.Policy.measurable_action_mem_historyFiltration_of_measurable_state theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:64
BanditRLProof.Policy.generatedActionTrace definition Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:98
BanditRLProof.Policy.measurable_generatedActionTrace_eval_of_measurable_state theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:110
BanditRLProof.Policy.generatedActionTraceSucc definition Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:130
BanditRLProof.Policy.generatedActionTraceSucc_zero theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:144
BanditRLProof.Policy.generatedActionTraceSucc_succ theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:159
BanditRLProof.Policy.generatedActionTraceSucc_succ_eq theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:171
BanditRLProof.Policy.measurable_generatedActionTraceSucc_eval_of_measurable_state theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:188
BanditRLProof.Policy.measurable_generatedActionTraceSucc_succ_mem_filtration_of_measurable_state theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:211
BanditRLProof.Policy.measurable_generatedActionTrace_eval_mem_filtration_of_measurable_state theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:237
BanditRLProof.Policy.measurable_generatedActionTrace_eval_mem_historyFiltration_of_measurable_state theorem Probability layer BanditRLProof.PolicyMeasurability Compiled BanditRLProof/PolicyMeasurability.lean:261
BanditRLProof.PosteriorKernel.MarkovPosteriorKernel structure Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:29
BanditRLProof.PosteriorKernel.ofKernel definition Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:44
BanditRLProof.PosteriorKernel.ofMeasureSelector definition Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:52
BanditRLProof.PosteriorKernel.ofMeasureSelector_apply theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:61
BanditRLProof.PosteriorKernel.ofCountableHistorySelector definition Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:76
BanditRLProof.PosteriorKernel.ofCountableHistorySelector_apply theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:85
BanditRLProof.PosteriorKernel.measurable_kernel theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:94
BanditRLProof.PosteriorKernel.measurable_apply_of_measurable_history theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:100
BanditRLProof.PosteriorKernel.measurable_eventProbability_of_measurable_history theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:112
BanditRLProof.PosteriorKernel.isProbabilityMeasure_apply theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:125
BanditRLProof.PosteriorKernel.apply_univ theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:134
BanditRLProof.PosteriorKernel.canonicalPosterior definition Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:153
BanditRLProof.PosteriorKernel.canonicalPosterior_kernel theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:162
BanditRLProof.PosteriorKernel.canonicalJointMeasure definition Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:171
BanditRLProof.PosteriorKernel.canonicalPosterior_kernel_ae_eq_condDistrib_of_pair_map_eq theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:194
BanditRLProof.PosteriorKernel.canonicalPosterior_kernel_ae_eq_condDistrib_fst_snd theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:247
BanditRLProof.PosteriorKernel.BayesianPosteriorSurface structure Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:268
BanditRLProof.PosteriorKernel.BayesianPosteriorSurface.posterior_isProbabilityMeasure_apply theorem Probability layer BanditRLProof.PosteriorKernel Compiled BanditRLProof/PosteriorKernel.lean:292
BanditRLProof.ProbabilityUnionBound.measure_biUnion_finset_le theorem Probability layer BanditRLProof.ProbabilityUnionBound Compiled BanditRLProof/ProbabilityUnionBound.lean:26
BanditRLProof.ProbabilityUnionBound.measure_biUnion_finset_le_of_uniform theorem Probability layer BanditRLProof.ProbabilityUnionBound Compiled BanditRLProof/ProbabilityUnionBound.lean:48
BanditRLProof.ProbabilityUnionBound.measure_iUnion_fintype_le_sum theorem Probability layer BanditRLProof.ProbabilityUnionBound Compiled BanditRLProof/ProbabilityUnionBound.lean:83
BanditRLProof.finset_sum_pullCount_eq_time theorem Foundations BanditRLProof.PullCountDecomposition Compiled BanditRLProof/PullCountDecomposition.lean:26
BanditRLProof.finset_sum_comp_pullCount theorem Foundations BanditRLProof.PullCountDecomposition Compiled BanditRLProof/PullCountDecomposition.lean:54
BanditRLProof.FiniteHorizonRL.CountCoordinate.rawCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:36
BanditRLProof.FiniteHorizonRL.CountCoordinate.policyMean definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:45
BanditRLProof.FiniteHorizonRL.CountCoordinate.measurable_rawCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:60
BanditRLProof.FiniteHorizonRL.CountCoordinate.deviation_eq_rawCount_sub_policyMean theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:74
BanditRLProof.FiniteHorizonRL.CountCoordinate.integral_rawCount_iidEpisodeBatchMeasure theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:86
BanditRLProof.FiniteHorizonRL.CountCoordinate.deviation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:177
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateKernelMean definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:221
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_coordinateKernelMean theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:231
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateKernelMean_eq_policyMean theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:241
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinatePrefixIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:259
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_coordinatePrefixIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:278
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:300
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateIncrement_stronglyAdapted_piLE theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:311
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_condDistrib_rawCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:325
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.condExpKernel_map_rawCount_eq_batchKernel theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:371
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateIncrement_zero_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:409
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateIncrement_succ_hasCondSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:431
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:553
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateConfidenceRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:558
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:564
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_cumulativeCoordinateDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:575
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_cumulativeCoordinateDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:589
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCountLocalDelta definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:630
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.adaptiveCumulativeCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:636
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurableSet_adaptiveCumulativeCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:650
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCountIndex_nonempty theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:662
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCountLocalDelta_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:671
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCountLocalDelta_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:681
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_adaptiveCumulativeCountBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:692
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateDeviation_abs_lt_of_not_mem_badEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:728
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateMeanAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:744
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateMean definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:757
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateRawCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:767
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateIncrement_eq_rawCount_sub_meanAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:775
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateDeviation_eq_rawCount_sub_mean theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:791
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateRawCount_visit theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:818
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateRawCount_transition theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:834
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateMeanAt_transition_eq_visit_mul_transition theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:849
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateMean_transition_eq_visit_mul_transition theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:877
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeEmpiricalTransitionMass_abs_sub_transition_lt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:900
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.adaptiveCumulativeTransitionCoordinateRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:986
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.AdaptiveCumulativeCountMartingaleCover definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:1005
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.coordinateConfidence_of_not_mem_adaptiveCumulativeCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:1029
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.adaptiveCumulativeCoordinateConfidenceContract_of_martingale definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:1124
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_adaptiveCumulativeCountMartingale_optimism_and_explicitRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:1157
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeCountMartingale_optimism_and_explicitRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeCountMartingaleConfidence.lean:1216
BanditRLProof.FiniteHorizonRL.exploratoryActionProbabilityFloor_eq_rate_mul_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:45
BanditRLProof.FiniteHorizonRL.exploratoryPathStateLowerNat_eq_rate_pow_mul_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:54
BanditRLProof.FiniteHorizonRL.exploratoryPathVisitLower_eq_rate_pow_mul_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:78
BanditRLProof.FiniteHorizonRL.ExploratoryPathUniformVisitFloor.scale_explorationRate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:96
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationScale definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:135
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:137
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationRounds definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:140
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationVisitFloor definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:143
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationScheduledEpisodes definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:147
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationAverageRecommendedExpectedRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:153
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationAverageExploratoryBehaviorExpectedRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:160
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationAverageEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:165
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationScale_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:175
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationRate_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:183
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationRate_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:191
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationRounds_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:201
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationVisitFloor_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:209
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationVisitFloor_mul_rounds theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:220
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationUniformVisitFloor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:251
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedScheduledAverageEnvelope_decayingExploration_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:265
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationAverageEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:295
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationBehaviorCharge_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:315
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationAverageExploratoryBehaviorBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:334
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationDeltaAndAverageExploratoryBehaviorBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:372
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationAverageExploratoryBehaviorRegretViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:390
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_decayingExplorationAverageExploratoryBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationBehaviorConsistency.lean:412
BanditRLProof.FiniteHorizonRL.MarkovPolicy.batchReturnVarianceProxy_coe theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:40
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeSuccessorReturnVarianceProxy_coe theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:57
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedSuccessorReturnConfidenceRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:76
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedSuccessorReturnConfidenceRadius_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:85
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedSuccessorReturnConfidenceRadius_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:98
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationReturnRadiusEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:142
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedSuccessorReturnConfidenceRadius_le_decayingEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:150
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationScheduledEpisodes_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:208
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationReturnRadiusEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:217
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationNormalizedReturnRadius_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:236
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationAverageRealizedBehaviorRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:255
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationRealizedFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:265
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationAverageRealizedBehaviorRegretBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:270
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationAverageRealizedBehaviorRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:290
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationRealizedFailureBudget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:305
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationRealizedFailureAndRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:311
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationAverageRealizedBehaviorRegretViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:330
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_decayingExplorationAverageRealizedBehaviorConsistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:361
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_decayingExplorationAverageRealizedBehaviorConsistency_allWindows theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeDecayingExplorationRealizedBehaviorConsistency.lean:482
BanditRLProof.FiniteHorizonRL.TransitionCountRadius structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:33
BanditRLProof.FiniteHorizonRL.TransitionCountRadius.linearDecay definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:41
BanditRLProof.FiniteHorizonRL.EpisodeBatchPrefix.cumulativeTransitionCountSummary definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:54
BanditRLProof.FiniteHorizonRL.EpisodeBatchPrefix.measurable_cumulativeTransitionCountSummary theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:64
BanditRLProof.FiniteHorizonRL.EpisodeBatchPrefix.cumulativeTransitionCountSummary_visitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:93
BanditRLProof.FiniteHorizonRL.cumulativeTransitionCountSummaryAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:113
BanditRLProof.FiniteHorizonRL.cumulativeTransitionCountSummaryAt_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:123
BanditRLProof.FiniteHorizonRL.cumulativeTransitionCountSummaryAt_visitCount_le_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:142
BanditRLProof.FiniteHorizonRL.TransitionCountRadius.radius_cumulativeVisitCount_succ_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:159
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.countRadiusOptimisticPlan definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:177
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.countRadiusOptimisticPlan_upperValueRemaining_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:194
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.countRadiusOptimisticPlan_selectedRadiusRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:281
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.countRadiusOptimisticPolicyTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:299
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.countRadiusOptimisticPolicyTable_toMarkovPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:308
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalOptimisticPlanAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:318
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalOptimisticRecommendedExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:327
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.successorTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:340
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.measurable_successorTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:350
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:362
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_successorPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:387
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeCoordinateConfidenceContract structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:407
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeCoordinateConfidence_optimism_and_recommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:426
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeCoordinateConfidenceContract.trajectoryMeasure_optimism_and_explicitRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEmpiricalOptimisticRegret.lean:485
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_realizedSuccessorCumulativeRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:37
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:51
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorExpectedCumulativeRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:64
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorExpectedAverageRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:77
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.abs_realizedSuccessorAverageRegret_le_of_expected_le_of_deviation_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:92
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_decayingExplorationEpisodewiseAverageAbsoluteRealizedBehaviorConsistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:136
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.DecayingExplorationEpisodewiseWindowSpace abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:262
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseWindowSource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:269
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseWindowMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:290
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseCommonMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:315
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseCommonMeasure_map_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:337
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseRealizedBehaviorRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:350
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.measurable_decayingExplorationEpisodewiseRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:362
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseCommonBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:378
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseCommonMeasure_badEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:393
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.abs_decayingExplorationEpisodewiseRealizedBehaviorRegretProcess_le_of_not_mem_badEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:446
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_decayingExplorationEpisodewiseCommonMeasure_marginals_and_realizedBehaviorRegret_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceConsistency.lean:488
BanditRLProof.FiniteHorizonRL.MDP.abs_cumulativeReward_le_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.abs_optimalInitialExpectedReturn_le_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:63
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_successor_rewardConsistent_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:82
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.abs_realizedSuccessorAverageRegret_le_two_mul_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:110
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_abs_realizedSuccessorAverageRegret_le_two_mul_horizon_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:168
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.integrable_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:187
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseCommonMeasure_abs_realizedBehaviorRegretProcess_le_two_mul_horizon_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:208
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.integrable_decayingExplorationEpisodewiseRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:246
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.measurableSet_decayingExplorationEpisodewiseCommonBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:268
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseExpectedAbsoluteRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:313
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseExpectedAbsoluteRealizedBehaviorRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:326
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseExpectedAbsoluteRealizedBehaviorRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:334
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseExpectedAbsoluteRealizedBehaviorRegretBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:345
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseExpectedAbsoluteRealizedBehaviorRegret_le_bound theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:360
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationRealizedFailureBudget_toReal_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:467
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseExpectedAbsoluteRealizedBehaviorRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:477
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_decayingExplorationEpisodewiseCommonMeasure_integrable_expectedAbsoluteRealizedBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceExpectedConsistency.lean:495
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.memLp_one_decayingExplorationEpisodewiseRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency.lean:30
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.eLpNorm_one_decayingExplorationEpisodewiseRealizedBehaviorRegretProcess_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency.lean:48
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.eLpNorm_one_decayingExplorationEpisodewiseRealizedBehaviorRegretProcess_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency.lean:71
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.eLpNorm_one_decayingExplorationEpisodewiseRealizedBehaviorRegretProcess_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency.lean:108
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseRealizedBehaviorRegretLp definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency.lean:145
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseRealizedBehaviorRegretLp_coeFn_ae_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency.lean:161
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseRealizedBehaviorRegretLp_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency.lean:179
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_decayingExplorationEpisodewiseCommonMeasure_memLp_eLpNorm_L1_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseCommonSpaceL1Consistency.lean:226
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_episode theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:38
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_episodeRowOfTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:49
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_iidEpisodeBatch_episode theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:63
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_iidEpisodeBatch_episodeReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:111
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integral_episodeReturn_iidEpisodeBatchMeasure theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:126
BanditRLProof.FiniteHorizonRL.MarkovPolicy.episodeReturnVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:142
BanditRLProof.FiniteHorizonRL.MarkovPolicy.episodeReturn_centered_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:148
BanditRLProof.FiniteHorizonRL.MarkovPolicy.episodewiseBatchReturnVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:178
BanditRLProof.FiniteHorizonRL.MarkovPolicy.episodeReturnVarianceProxy_coe theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:185
BanditRLProof.FiniteHorizonRL.MarkovPolicy.episodewiseBatchReturnVarianceProxy_coe theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:197
BanditRLProof.FiniteHorizonRL.MarkovPolicy.totalReturn_centered_episodewise_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:204
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorReturnIncrement_succ_episodewise_hasCondSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:253
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.episodewiseCumulativeSuccessorReturnVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:369
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.episodewiseCumulativeSuccessorReturnVarianceProxy_coe theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:380
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.episodewiseBatchReturnVarianceProxy_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:397
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_episodewiseCumulativeSuccessorReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:409
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.episodewiseSuccessorReturnDeviationBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:460
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurableSet_episodewiseSuccessorReturnDeviationBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:472
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_episodewiseSuccessorReturnDeviationBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:482
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_expected_to_realized_successor_average_regret_episodewise_transport theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:500
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.episodewiseNormalizedSuccessorReturnConfidenceRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:591
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.episodewiseNormalizedSuccessorReturnConfidenceRadius_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:601
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.episodewiseNormalizedSuccessorReturnConfidenceRadius_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:614
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.episodewiseNormalizedSuccessorReturnConfidenceRadius_le_normalized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:671
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.episodewiseNormalizedSuccessorReturnConfidenceRadius_le_decayingEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:698
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationEpisodewiseNormalizedReturnRadius_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:717
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationEpisodewiseAverageRealizedBehaviorRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:736
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationEpisodewiseAverageRealizedBehaviorRegretBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:745
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationEpisodewiseAverageRealizedBehaviorRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:765
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.decayingExplorationEpisodewiseRealizedFailureAndRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:777
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.decayingExplorationEpisodewiseAverageRealizedBehaviorRegretViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:796
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_decayingExplorationEpisodewiseAverageRealizedBehaviorConsistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:828
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_decayingExplorationEpisodewiseAverageRealizedBehaviorConsistency_allWindows theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeEpisodewiseRealizedBehaviorConsistency.lean:986
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryActionPMF_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:30
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.integral_exploratoryActionPMF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:43
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.selected_sub_integral_exploratoryActionPMF_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:99
BanditRLProof.FiniteHorizonRL.MDP.bellmanQ_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:151
BanditRLProof.FiniteHorizonRL.MDP.transitionValue_sub_le_const theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:172
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueRemaining_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:199
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.toMarkovPolicy_bellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:234
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryPolicy_bellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:247
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.toMarkovPolicy_valueRemaining_sub_exploratoryPolicy_valueRemaining_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:269
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryPolicy_expectedRegret_le_toMarkovPolicy_expectedRegret_add_charge theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:356
BanditRLProof.FiniteHorizonRL.exploratoryBehaviorRegretCharge definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:438
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalOptimisticExploratoryBehaviorExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:445
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalOptimisticAverageExploratoryBehaviorExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:458
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalOptimisticExploratoryBehaviorExpectedRegret_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:471
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalOptimisticAverageExploratoryBehaviorExpectedRegret_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:520
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingDeltaScheduledAverageExploratoryBehaviorExpectedRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:563
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingDeltaScheduledAverageExploratoryBehaviorBound_tendsto_charge theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:570
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_policyAt_succ_eq_cumulativeOptimisticExploratoryPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:594
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.vanishingDeltaScheduledAverageExploratoryBehaviorRegretViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:609
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_vanishingDeltaScheduledAverageExploratoryBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeExploratoryBehaviorRegret.lean:635
BanditRLProof.FiniteHorizonRL.RewardSumSummary abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:42
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalModelState abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:50
BanditRLProof.FiniteHorizonRL.AggregateVisitCountSummary abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:54
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.aggregateVisitCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:59
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.measurable_aggregateVisitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:69
BanditRLProof.FiniteHorizonRL.EpisodeBatchPrefix.cumulativeRewardSumSummary definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:87
BanditRLProof.FiniteHorizonRL.EpisodeBatchPrefix.measurable_rewardSum_coordinate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:97
BanditRLProof.FiniteHorizonRL.EpisodeBatchPrefix.measurable_cumulativeRewardSumSummary theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:121
BanditRLProof.FiniteHorizonRL.EpisodeBatchPrefix.cumulativeEmpiricalModelState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:140
BanditRLProof.FiniteHorizonRL.EpisodeBatchPrefix.measurable_cumulativeEmpiricalModelState theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:149
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalModelStateAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:160
BanditRLProof.FiniteHorizonRL.measurable_adaptiveCumulativeEmpiricalModelStateAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:169
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalModelStateAt_transitionCount_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:179
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalModelStateAt_rewardSum_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:196
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalModelStateAt_visitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:221
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeAggregateVisitCountAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:235
BanditRLProof.FiniteHorizonRL.measurable_adaptiveCumulativeAggregateVisitCountAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:243
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeAggregateVisitCountAt_eq_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:253
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeAggregateVisitCountAt_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:269
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalModelState.empiricalReward definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:283
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalModelState.empiricalReward_of_visitCount_eq_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:294
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.totalSteps definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:305
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.confidenceNumerator definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:309
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.logFactor definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:319
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.one_le_confidenceNumerator_div theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:327
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.logFactor_eq_paper theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:349
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.logFactor_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:365
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.scale definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:372
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.scale_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:380
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.countRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:392
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.countRadius_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:404
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.countRadius_of_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:413
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.source definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:430
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.source_successorPolicy_eq_optimisticPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:461
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.source_policyAt_succ_eq_optimisticPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:480
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.source_policyAt_succ_eq_modelState_optimisticPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeHoeffdingUCBVI.lean:495
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledEpisodeThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledEpisodes definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:44
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledAverageEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:53
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtLogFactor_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:60
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledEpisodeThreshold_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:77
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledEpisodes_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:96
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledEpisodeThreshold_lt_episodes theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:108
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtEpisodeThreshold_lt_scheduledEpisodes theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:130
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtLogFactor_lt_scheduledEpisodeVisitMass theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:146
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledAverageBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:163
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledAverageBound_le_envelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:182
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledAverageEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:297
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScheduledAverageBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:315
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_scheduledAverageRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageConsistency.lean:346
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeExploratoryEpisodeCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate.lean:29
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtAverageRecommendedExpectedRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate.lean:33
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtAverageRecommendedExpectedRegretBound_eq_totalEpisodes theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate.lean:47
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeEmpiricalOptimisticAverageRecommendedExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate.lean:117
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_normalizedAverageRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtAverageRate.lean:133
BanditRLProof.FiniteHorizonRL.TransitionCountRadius.inverseSqrt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:41
BanditRLProof.FiniteHorizonRL.TransitionCountRadius.inverseSqrt_radius_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:71
BanditRLProof.FiniteHorizonRL.TransitionCountRadius.inverseSqrt_radius_of_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:76
BanditRLProof.FiniteHorizonRL.TransitionCountRadius.cappedInverseSqrt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:87
BanditRLProof.FiniteHorizonRL.TransitionCountRadius.cappedInverseSqrt_radius_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:114
BanditRLProof.FiniteHorizonRL.TransitionCountRadius.cappedInverseSqrt_radius_of_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:119
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativePathVisitExpectedFloor definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:131
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativePathVisitLowerMargin definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:136
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtRadiusEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:144
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.CumulativeInverseSqrtPathCalibration structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:155
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_coordinateMeanAt_visit_ge_pathFloor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:187
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_cumulativeCoordinateMean_visit_ge_pathFloor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:222
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_cumulativePathVisitLowerMargin_lt_visitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:257
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_adaptiveCumulativeCountMartingaleCover_of_pathSupport_inverseSqrtCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:293
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.adaptiveCumulativeEmpiricalOptimisticPlanAt_selectedRadiusRemaining_le_inverseSqrtEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:418
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_explicitRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtCalibration.lean:483
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtLogFactor definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:30
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtCoverCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtCalibrationEpisodeThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:44
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeCoordinateConfidenceRadius_sq_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:54
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtLogFactor_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:83
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.half_cumulativePathVisitExpectedFloor_lt_lowerMargin_of_episodeThreshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:103
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtPathCalibration_of_episodeThreshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:175
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtEnvelopeSumBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:352
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.sum_cumulativeInverseSqrtRadiusEnvelope_le_explicit theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:362
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtRecommendedExpectedRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:462
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.sum_horizon_mul_two_cumulativeInverseSqrtRadiusEnvelope_le_explicit theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:469
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_closedFormRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtExplicitRate.lean:514
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingAverageConfidenceDelta definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:33
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingDeltaScheduledEpisodes definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:37
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingDeltaScheduledAverageRecommendedExpectedRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:43
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingAverageConfidenceDelta_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:55
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingAverageConfidenceDelta_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:66
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingAverageConfidenceDelta_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:80
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingAverageConfidenceDelta_ennreal_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:93
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingDeltaScheduledAverageBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:101
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingDeltaScheduledAverageBound_le_envelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:111
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingDeltaScheduledAverageBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:123
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.vanishingDeltaAndScheduledAverageBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:140
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.vanishingDeltaScheduledAverageRegretViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:162
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_vanishingDeltaScheduledAverageRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:188
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_vanishingDeltaScheduledAverageRecommendedExpectedRegret_allWindows theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtHighProbabilityAverageConsistency.lean:309
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScale definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:29
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtEpisodeThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:37
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtCountRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:45
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtRecommendedExpectedRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:55
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScale_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:66
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtScale_cover theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:74
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtCalibrationEpisodeThreshold_le_normalized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:106
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeInverseSqrtCalibrationEpisodeThreshold_lt_of_normalizedThreshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:145
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtPathCalibration_of_episodeThreshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:161
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.normalizedCumulativeInverseSqrtRecommendedExpectedRegretBound_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:185
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_normalizedRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeInverseSqrtNormalizedRate.lean:221
BanditRLProof.FiniteHorizonRL.MDP.traceStateAtFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:37
BanditRLProof.FiniteHorizonRL.MDP.traceStateAtFrom_tail theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:42
BanditRLProof.FiniteHorizonRL.MDP.cumulativeRewardFrom_eq_sum_traceReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:53
BanditRLProof.FiniteHorizonRL.EpisodeBatch.episodeReturn definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:74
BanditRLProof.FiniteHorizonRL.EpisodeBatch.totalReturn definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:78
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_episodeReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:82
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_totalReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:90
BanditRLProof.FiniteHorizonRL.EpisodeBatch.abs_episodeReturn_le_horizon_of_rewardConsistent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:95
BanditRLProof.FiniteHorizonRL.EpisodeBatch.abs_totalReturn_le_of_rewardConsistent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:112
BanditRLProof.FiniteHorizonRL.MDP.episodeReturn_episodeBatchOfTrajectories theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:132
BanditRLProof.FiniteHorizonRL.MDP.totalReturn_episodeBatchOfTrajectories theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:144
BanditRLProof.FiniteHorizonRL.MarkovPolicy.batchReturnVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:159
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integral_cumulativeReward_eval_iidTrajectoryFamilyMeasure theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:165
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integral_totalReturn_iidEpisodeBatchMeasure theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:183
BanditRLProof.FiniteHorizonRL.MarkovPolicy.totalReturn_centered_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:210
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorReturnKernelMean definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:244
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_successorReturnKernelMean theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:251
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorReturnKernelMean_eq_selectedPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:258
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorReturnPrefixIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:273
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_successorReturnPrefixIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:287
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorReturnIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:307
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorReturnIncrement_stronglyAdapted_piLE theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:315
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_condDistrib_totalReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:327
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.condExpKernel_map_totalReturn_eq_batchKernel theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:370
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorReturnIncrement_succ_hasCondSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:409
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeSuccessorReturnVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:523
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeSuccessorReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:530
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.batchReturnVarianceProxy_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:537
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_cumulativeSuccessorReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:553
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.optimalInitialExpectedReturn definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:600
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorExpectedCumulativeRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:605
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorExpectedAverageRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:613
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.realizedSuccessorCumulativeRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:620
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.realizedSuccessorAverageRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:629
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorReturnDeviationBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:637
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_cumulativeSuccessorReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:648
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurableSet_successorReturnDeviationBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:659
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorReturnIncrement_succ_eq_totalReturn_sub_selectedPolicyMean theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:668
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.cumulativeSuccessorReturnDeviation_eq_fin_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:684
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.realizedSuccessorCumulativeRegret_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:701
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.realizedSuccessorAverageRegret_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:733
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_successorReturnDeviationBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:750
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_expected_to_realized_successor_average_regret_transport theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:767
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_successorExpectedCumulativeRegret_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:854
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_successorExpectedAverageRegret_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:873
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_cumulativeInverseSqrtPathSupport_optimism_and_decayingExplorationAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeRealizedBehaviorRegret.lean:890
BanditRLProof.measurable_prod_of_countable_left theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:14
MeasureTheory.Measure.compProd_map_dependent lemma Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:45
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_condDistrib_historyBatchStatistic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:83
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.condExpKernel_map_historyBatchStatistic_eq_batchKernel theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:175
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bellmanInflation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:222
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bellmanWeightCap definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:226
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bellmanInflation_one_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:228
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bellmanInflation_pow_le_cap theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:235
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.normalizedBellmanWeight definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:271
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.normalizedBellmanChargeWeight definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:276
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.normalizedBellmanChargeWeight_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:280
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.normalizedBellmanChargeWeight_mul_inflation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:301
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.normalizedBellmanWeight_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:309
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedSuccessorGapFeatureOfSummaries definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:333
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedSuccessorGapFeatureOfSummaries_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:351
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorBellmanStatisticOfSummaries definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:378
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_successorBellmanStatisticOfSummaries theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:392
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorBellmanHistoryBatchStatistic definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:412
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_successorBellmanHistoryBatchStatistic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:419
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.recurrentSuccessorBellmanInnovation_compensated_hasCondMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:433
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorBellmanInnovationOfSummaries definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:581
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_successorBellmanInnovationOfSummaries theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:594
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorBellmanInnovationOfHistoryBatch definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:614
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_successorBellmanInnovationOfHistoryBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:621
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentBellmanInnovationPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:634
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_recurrentBellmanInnovationPrefix theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:646
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentBellmanInnovationProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:666
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentBellmanInnovationVarianceProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:675
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentBellmanInnovation_compensated_stronglyAdapted theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:682
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentBellmanInnovation_zero_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:717
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.trajectoryMeasure_recurrentBellmanInnovation_sum_ge_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAdaptiveBellmanMartingale.lean:742
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.aggregateTransitionCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:33
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.measurable_aggregateTransitionCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:42
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.sum_aggregateTransitionCount_eq_aggregateVisitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:57
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.aggregateEmpiricalTransitionPMF definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:68
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.aggregateEmpiricalTransitionPMF_of_aggregateVisitCount_eq_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:103
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.aggregateEmpiricalTransitionPMF_apply_of_aggregateVisitCount_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:111
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.aggregateEmpiricalTransitionKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:121
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.aggregateEmpiricalTransitionKernel_isMarkov theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:128
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeAggregateTransitionCountAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:142
BanditRLProof.FiniteHorizonRL.measurable_adaptiveCumulativeAggregateTransitionCountAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:150
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeAggregateTransitionCountAt_eq_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:166
BanditRLProof.FiniteHorizonRL.adaptiveCumulativeAggregateTransitionCountAt_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:186
BanditRLProof.FiniteHorizonRL.sum_adaptiveCumulativeAggregateTransitionCountAt_eq_visitCountAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAggregateTransition.lean:205
BanditRLProof.FiniteHorizonRL.MDP.measurable_trajectoryStateAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAlignment.lean:29
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.trajectoryMeasure_action_eq_table_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAlignment.lean:45
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.iidEpisodeBatchMeasure_successorBatchAligned_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAlignment.lean:102
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_trajectoryMeasure_successorBatchAligned_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAlignment.lean:195
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_trajectoryMeasure_all_successorBatchAligned_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIAlignment.lean:310
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeDeterministicGapInnovationFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:34
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeDeterministicGapInnovationFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:49
BanditRLProof.FiniteHorizonRL.MDP.actionStateKernel_deterministicGapInnovation_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:78
BanditRLProof.FiniteHorizonRL.MDP.trajectoryKernelRemaining_deterministicGapInnovation_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:143
BanditRLProof.FiniteHorizonRL.MDP.trajectoryMeasure_deterministicGapInnovation_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:269
BanditRLProof.FiniteHorizonRL.MDP.abs_sampledCumulativeDeterministicGapInnovationFrom_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:326
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeTransitionGapInnovationFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:385
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeTransitionGapInnovationFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:400
BanditRLProof.FiniteHorizonRL.MDP.abs_sampledCumulativeTransitionGapInnovationFrom_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:432
BanditRLProof.FiniteHorizonRL.MDP.actionStateKernel_transitionGapInnovation_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:491
BanditRLProof.FiniteHorizonRL.MDP.trajectoryKernelRemaining_transitionGapInnovation_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:581
BanditRLProof.FiniteHorizonRL.MDP.trajectoryMeasure_transitionGapInnovation_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:715
BanditRLProof.FiniteHorizonRL.EpisodeBatch.reconstructedInitialState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:775
BanditRLProof.FiniteHorizonRL.EpisodeBatch.reconstructedStepTrace definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:782
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_reconstructedInitialState theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:788
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_reconstructedStepTrace theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:798
BanditRLProof.FiniteHorizonRL.EpisodeBatch.cumulativeDeterministicGapInnovation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:810
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_cumulativeDeterministicGapInnovation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:820
BanditRLProof.FiniteHorizonRL.EpisodeBatch.cumulativeDeterministicGapInnovation_episodeBatchOfTrajectories theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:833
BanditRLProof.FiniteHorizonRL.EpisodeBatch.cumulativeTransitionGapInnovation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:859
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_cumulativeTransitionGapInnovation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:869
BanditRLProof.FiniteHorizonRL.EpisodeBatch.cumulativeTransitionGapInnovation_episodeBatchOfTrajectories theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:883
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.iidEpisodeBatchMeasure_one_cumulativeDeterministicGapInnovation_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:915
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchMeasure_one_cumulativeTransitionGapInnovation_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBellmanInnovation.lean:994
BanditRLProof.FiniteHorizonRL.MDP.transitionCoordinateVariance definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:30
BanditRLProof.FiniteHorizonRL.MDP.transitionCoordinateVariance_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:37
BanditRLProof.FiniteHorizonRL.MDP.integral_sq_indicator_sub_transitionMass theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:46
BanditRLProof.FiniteHorizonRL.MDP.transitionResidualHead_variance_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:99
BanditRLProof.FiniteHorizonRL.MDP.actionStateKernel_transitionResidualHead_variance_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:210
BanditRLProof.FiniteHorizonRL.MDP.trajectoryKernelRemaining_transitionResidual_variance_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:270
BanditRLProof.FiniteHorizonRL.MDP.trajectoryMeasure_transitionResidual_variance_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:412
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchMeasure_one_aggregateTransitionResidual_variance_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:481
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionResidual_succ_variance_compensated_hasCondMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:572
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionResidual_zero_variance_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:656
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measure_aggregateTransitionResidualSum_ge_inter_visitSum_le_variance theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:689
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measure_abs_aggregateTransitionResidualSum_ge_inter_visitSum_le_variance theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIBernsteinConfidence.lean:744
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedBatchAggregateVisitIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:25
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.batchedPrefixCount_generatedBatchAggregateVisitIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:30
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedBatchAggregateVisitIncrement_le_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:43
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.SuccessorBatchAligned definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:53
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorBatchAligned_step theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:68
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedBatchAggregateVisitIncrement_eq_indicatorSum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:88
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_generatedBatchAggregateVisitIncrement_eq_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:109
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedPairLocalCharge definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:150
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedPairLocalCharge_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:167
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorLocalCharge_eq_generatedPairLocalCharge_of_aligned theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:182
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_successorLocalCharge_eq_sum_pairIncrement_mul_charge_of_aligned theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:222
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.remainingGlobalStage definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:275
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorLocalCharge_eq_of_remaining_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:280
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorStageLocalCharge definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:296
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorWeightedChargeFrom_eq_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:305
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorCanonicalWeightedCharge_eq_successorWeightedChargeSum_of_aligned theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:378
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorCanonicalWeightedCharge_le_sum_pairIncrement_mul_charge_of_aligned theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:407
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.totalGeneratedPairCharge definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:437
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedPairChargeTerm_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:445
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_range_succ_shift_le_sum_range theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:454
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_successorCanonicalWeightedCharge_le_totalGeneratedPairCharge theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:471
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.min_add_le_add_min theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:512
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.reciprocalChargeThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:521
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_generatedPairCharge_le_accounting theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:527
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_generatedPairCharge_le_explicit theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:654
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.one_le_logFactor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:760
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.batchedPrefixCount_generatedBatchAggregateVisitIncrement_le_totalSteps theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:803
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.log_max_batchedPrefixCount_le_logFactor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:822
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_batchedPrefixCount_generatedBatchAggregateVisitIncrement_eq_totalSteps theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:888
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_sqrt_batchedPrefixCount_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:904
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.totalGeneratedPairCharge_le_explicit theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIChargeSummation.lean:942
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.QTable abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:39
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.initialQTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:43
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.cumulativeSummaryOfSequence definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:47
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedValueRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:59
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedQRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:85
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedQTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:106
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedQRemaining_of_aggregateVisitCount_eq_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:115
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedQRemaining_of_aggregateVisitCount_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:126
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedPolicyTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:149
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedQTable_le_selected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:160
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_clippedPolicyTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:174
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentQTableOfSummaries definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:183
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentPolicyTableOfSummaries definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:194
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.prefixTransitionSummaries definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:205
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_prefixTransitionSummaries theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:214
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSuccessorTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:225
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_recurrentSuccessorTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:234
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentInitialTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:257
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:268
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_policyAt_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:293
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_policyAt_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIClippedPlanner.lean:304
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bernsteinTilt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning.lean:9
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bernsteinCoordinateThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning.lean:13
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bernsteinTilt_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning.lean:17
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bernsteinTilt_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning.lean:28
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bernsteinTilt_abs_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning.lean:34
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bernsteinTilt_exponent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIConfidenceTuning.lean:41
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.aggregateEmpiricalTransitionKernel_real_singleton_of_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment.lean:29
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bernsteinCoordinateThreshold_mul_probability_div_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment.lean:51
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.abs_sum_weight_mul_massError_le_transitionValue_div_thirtyTwo_add theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment.lean:116
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.abs_empiricalTransitionMass_sub_lt_bernstein theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment.lean:286
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.abs_empiricalTransition_integral_sub_le_transitionValue_div_thirtyTwo_add theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICoordinateAlignment.lean:354
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.batchedPrefixCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:18
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.batchedPrefixCount_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:21
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.batchedPrefixCount_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:25
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.batchedPrefixCount_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:30
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_range_forwardDifference theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_low_batchedIncrement_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:47
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.batched_ratio_le_two_log_increment theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:74
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_high_batchedRatio_le_log theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:100
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.batched_inverseSqrt_step theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:142
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_positive_batchedInvSqrt_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:218
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_positive_batchedMinReciprocal_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVICounting Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVICounting.lean:396
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueRemaining_nonneg_of_reward_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret.lean:22
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedQTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret.lean:45
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedPolicyTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret.lean:54
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_policyAt_eq_generatedPolicyTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret.lean:65
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedEpisodeInitialState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret.lean:80
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedEpisodePseudoRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret.lean:88
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.cumulativeEpisodePseudoRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret.lean:101
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.generatedEpisodePseudoRegret_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret.lean:112
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.cumulativeEpisodePseudoRegret_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIEpisodeRegret.lean:145
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_generatedPolicyTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret.lean:29
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_generatedEpisodeInitialState theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret.lean:48
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_generatedEpisodePseudoRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret.lean:60
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.measurable_cumulativeEpisodePseudoRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret.lean:89
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.integral_cumulativeEpisodePseudoRegret_recurrentSource_le_canonicalRegretBound_add_failure theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIExpectedRegret.lean:104
BanditRLProof.FiniteHorizonRL.MDP.optimalValueAt_eq_of_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:29
BanditRLProof.FiniteHorizonRL.MDP.optimalValueAt_nonneg_of_reward_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:38
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.decisionStageRemaining_succ_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:51
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedQRemaining_eq_of_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:61
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedValueRemaining_succ_eq_selectedQ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:74
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedQTable_le_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:117
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedValueRemaining_le_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:133
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.optimalValueAt_le_clippedValueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:152
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedValueRemaining_sub_policyValueRemaining_le_of_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:216
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedPolicyGapRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:318
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedPolicyGapRemaining_le_of_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:330
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.selectedUpperTransitionModelError_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:374
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.selectedPolicyGap_le_of_actual_count theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVILocalBellman Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVILocalBellman.lean:590
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bellmanInnovationThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning.lean:22
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bellmanInnovationTilt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning.lean:29
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bellmanInnovationThreshold_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bellmanInnovationTilt_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning.lean:46
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.bellmanInnovationTilt_exponent_le_neg_two_logFactor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning.lean:66
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_trajectoryMeasure_bellmanInnovation_sum_ge_threshold_le_fifth theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIMartingaleTuning.lean:105
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.integral_optimalValue_sub_eq_two_mul_horizon_mul_integral_probe_sub theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimalTailAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimalTailAlignment.lean:23
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.abs_empiricalTransition_optimalValue_sub_lt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimalTailAlignment Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimalTailAlignment.lean:97
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.optimalQAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimism.lean:20
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.QDominatesOptimal definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimism.lean:27
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.optimalQAt_le_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimism.lean:32
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.initialQTable_dominatesOptimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimism.lean:77
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.HasOptimalTailConfidence definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimism.lean:87
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.clippedQTable_dominatesOptimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimism.lean:103
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.adaptiveCumulativeAggregateVisitCountAt_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimism.lean:254
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.hasOptimalTailConfidence_of_not_mem_simultaneousTransitionFailureEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIOptimism.lean:276
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.card_bernsteinCoordinateIndex theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget.lean:22
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.card_optimalTailIndex theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget.lean:40
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.exp_neg_two_mul_logFactor_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget.lean:60
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.exp_neg_two_mul_logFactor_sq_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget.lean:90
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.ofReal_card_mul_two_mul_exp_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget.lean:103
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.simultaneousTransitionTailBudget_le_fifth theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget.lean:118
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_trajectoryMeasure_simultaneousTransitionFailureEvent_le_fifth theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIProbabilityBudget.lean:234
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.cumulativeSummaryOfSequence_prefixTransitionSummaries_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRecurrentOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRecurrentOptimism.lean:23
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.recurrentQTableOfTrajectory_dominatesOptimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRecurrentOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRecurrentOptimism.lean:41
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.recurrentSuccessor_selectedQ_ge_optimalQ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRecurrentOptimism Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRecurrentOptimism.lean:98
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorPreviousQ definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:22
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorSummary definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:31
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorPolicyTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:38
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorPolicyGapRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:49
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorLocalCharge definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:63
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorPolicyGapRemaining_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:83
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorLocalCharge_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:143
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.normalizedBellmanRemainingWeight definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:158
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.normalizedBellmanRemainingWeight_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:162
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.normalizedBellmanRemainingWeight_succ_eq_chargeWeight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:167
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.normalizedBellmanRemainingWeight_eq_stageWeight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:176
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorWeightedChargeFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:191
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorCanonicalWeightedCharge definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:207
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorWeightedChargeSum definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:217
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorWeightedChargeSum_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:227
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.successorWeightedVisitedGap definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:240
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.successorPolicyGapRemaining_le_inflation_mul_transition_add_charge theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:254
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.clippedSuccessorGapFeatureOfSummaries_eq_weight_mul_gap theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:410
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.normalizedGap_le_weightedChargeFrom_add_deterministicInnovation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:460
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.successorPolicyGapRemaining_le_cap_mul_charge_add_innovation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:571
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.recurrentSource_generatedEpisodePseudoRegret_le_successorPolicyGapRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:613
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.recurrentBellmanInnovationProcess_succ_eq_canonical theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:684
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.recurrentSource_generatedSuccessorPseudoRegret_le_charge_add_innovation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVIRegretDecomposition.lean:700
BanditRLProof.FiniteHorizonRL.MDP.transitionResidualHead definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:37
BanditRLProof.FiniteHorizonRL.MDP.transitionVisitHead definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:46
BanditRLProof.FiniteHorizonRL.MDP.transitionResidualFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:52
BanditRLProof.FiniteHorizonRL.MDP.transitionVisitFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:63
BanditRLProof.FiniteHorizonRL.MDP.measurable_transitionResidualFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:73
BanditRLProof.FiniteHorizonRL.MDP.measurable_transitionVisitFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:82
BanditRLProof.FiniteHorizonRL.MDP.transitionResidualHead_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:90
BanditRLProof.FiniteHorizonRL.MDP.actionStateKernel_transitionResidualHead_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:180
BanditRLProof.FiniteHorizonRL.MDP.trajectoryKernelRemaining_transitionResidual_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:242
BanditRLProof.FiniteHorizonRL.MDP.transitionResidualFrom_eq_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:379
BanditRLProof.FiniteHorizonRL.MDP.transitionVisitFrom_eq_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:406
BanditRLProof.FiniteHorizonRL.MDP.transitionResidualFrom_eq_aggregateCounts theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:435
BanditRLProof.FiniteHorizonRL.MDP.transitionVisitFrom_eq_aggregateVisitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:496
BanditRLProof.FiniteHorizonRL.MDP.trajectoryMeasure_transitionResidual_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:520
BanditRLProof.FiniteHorizonRL.EpisodeBatch.aggregateTransitionResidual definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:582
BanditRLProof.FiniteHorizonRL.EpisodeBatch.aggregateVisitReal definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:590
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_aggregateTransitionResidual theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:596
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_aggregateVisitReal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:630
BanditRLProof.FiniteHorizonRL.EpisodeBatch.aggregateVisitCount_le_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:646
BanditRLProof.FiniteHorizonRL.EpisodeBatch.abs_aggregateTransitionResidual_le_two_mul_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:679
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchMeasure_one_aggregateTransitionResidual_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:723
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.batchPrefixFiltration definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:811
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.hasCondMGFUpperBoundAt_of_condExpKernel_map_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:833
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.hasCondMGFUpperBoundAt_congr_measurableSpace theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:873
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionResidualPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:890
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateVisitPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:900
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_aggregateTransitionResidualPrefix theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:909
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_aggregateVisitPrefix theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:922
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionResidualIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:933
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateVisitIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:943
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_aggregateTransitionResidualIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:953
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_aggregateVisitIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:964
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionResidual_compensated_stronglyAdapted_piLE theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:975
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_condDistrib_batchStatistic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:1008
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.condExpKernel_map_batchStatistic_eq_batchKernel theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:1055
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.integrable_exp_mul_aggregateTransitionResidual_compensatedIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:1095
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionResidual_succ_compensated_hasCondMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:1179
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionResidual_zero_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:1262
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.sum_aggregateTransitionResidualIncrement_eq_prefixAggregateResidual theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:1295
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.sum_aggregateVisitIncrement_eq_prefixAggregateVisitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:1342
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measure_aggregateTransitionResidualSum_ge_inter_visitSum_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:1366
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measure_abs_aggregateTransitionResidualSum_ge_inter_visitSum_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISameSourceConfidence.lean:1419
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.BernsteinCoordinateIndex structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.OptimalTailIndex structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:45
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.bernsteinCoordinateFailureEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:55
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.optimalTailFailureEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:72
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.simultaneousTransitionFailureEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:89
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.trajectoryMeasure_bernsteinCoordinateFailureEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:100
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.functionalTilt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:152
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.functionalTilt_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:155
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.functionalTilt_exponent_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:162
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.trajectoryMeasure_optimalTailFailureEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:177
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.trajectoryMeasure_simultaneousTransitionFailureEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:214
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.abs_coordinateResidual_lt_of_not_mem_simultaneousTransitionFailureEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:260
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.AdaptiveEpisodeBatchSource.abs_optimalTailResidual_lt_of_not_mem_simultaneousTransitionFailureEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVISimultaneousConfidence.lean:287
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.canonicalRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:28
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.canonicalRegretBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:38
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.alignmentFailureEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:47
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.canonicalFailureEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:56
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_trajectoryMeasure_alignmentFailureEvent_eq_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:72
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_trajectoryMeasure_canonicalFailureEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:96
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sum_shift_recurrentBellmanInnovation_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:157
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.sqrt_totalSteps_mul_card_eq_paper theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:174
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.cumulativeEpisodePseudoRegret_le_canonicalRegretBound_of_not_mem theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:188
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeHoeffdingUCBVI.recurrentSource_trajectoryMeasure_cumulativeEpisodePseudoRegret_gt_canonicalRegretBound_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITerminal Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITerminal.lean:403
BanditRLProof.FiniteHorizonRL.MDP.optimalTailProbe definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:34
BanditRLProof.FiniteHorizonRL.MDP.optimalTailProbe_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:41
BanditRLProof.FiniteHorizonRL.MDP.transitionFunctionalResidualHead definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:75
BanditRLProof.FiniteHorizonRL.MDP.transitionFunctionalResidualFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:83
BanditRLProof.FiniteHorizonRL.MDP.measurable_transitionFunctionalResidualFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:93
BanditRLProof.FiniteHorizonRL.MDP.transitionValue_eq_sum_measureReal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:106
BanditRLProof.FiniteHorizonRL.MDP.transitionFunctionalResidualHead_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:123
BanditRLProof.FiniteHorizonRL.MDP.transitionFunctionalResidualFrom_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:154
BanditRLProof.FiniteHorizonRL.MDP.transitionFunctionalResidualHead_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:173
BanditRLProof.FiniteHorizonRL.MDP.actionStateKernel_transitionFunctionalResidualHead_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:231
BanditRLProof.FiniteHorizonRL.MDP.trajectoryKernelRemaining_transitionFunctionalResidual_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:288
BanditRLProof.FiniteHorizonRL.MDP.trajectoryMeasure_transitionFunctionalResidual_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:428
BanditRLProof.FiniteHorizonRL.MDP.transitionFunctionalResidualFrom_eq_aggregateFunctionalResidual theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:487
BanditRLProof.FiniteHorizonRL.EpisodeBatch.aggregateTransitionFunctionalResidual definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:510
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_aggregateTransitionFunctionalResidual theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:517
BanditRLProof.FiniteHorizonRL.EpisodeBatch.abs_aggregateTransitionFunctionalResidual_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:529
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.integral_aggregateEmpiricalTransitionKernel_eq_sum_div theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:570
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchMeasure_one_aggregateTransitionFunctionalResidual_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:598
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionFunctionalResidualPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:688
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionFunctionalResidualIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:697
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_aggregateTransitionFunctionalResidualPrefix theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:707
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurable_aggregateTransitionFunctionalResidualIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:721
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionFunctionalResidual_compensated_stronglyAdapted_piLE theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:733
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.integrable_exp_mul_aggregateTransitionFunctionalResidual_compensatedIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:758
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionFunctionalResidual_succ_compensated_hasCondMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:840
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionFunctionalResidual_zero_compensated_hasMGFUpperBoundAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:922
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.sum_aggregateTransitionFunctionalResidualIncrement_eq_prefixResidual theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:954
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.aggregateTransitionFunctionalResidual_eq_count_mul_transitionValue_sub theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:986
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measure_abs_aggregateTransitionFunctionalResidualSum_ge_inter_visitSum_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveCumulativeUCBVITransitionValueConfidence.lean:1056
BanditRLProof.FiniteHorizonRL.EpisodeBatch.transitionCountSummary_visitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:43
BanditRLProof.FiniteHorizonRL.EpisodeBatch.transitionCountSummary_empiricalTransitionPMF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:55
BanditRLProof.FiniteHorizonRL.EpisodeBatch.transitionCountSummary_empiricalTransitionKernel_real_singleton theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:83
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.optimisticPlan_upperValueRemaining_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:108
BanditRLProof.FiniteHorizonRL.MarkovPolicy.EmpiricalOptimisticCalibration structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:194
BanditRLProof.FiniteHorizonRL.MarkovPolicy.empiricalOptimisticPlanCoordinateConfidence_of_not_mem definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:217
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryActionPMF definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:277
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.explorationRate_mul_inv_card_le_exploratoryActionPMF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:288
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryPolicy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:302
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryIIDEpisodeBatchKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:317
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryIIDEpisodeBatchKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:329
BanditRLProof.FiniteHorizonRL.adaptiveEmpiricalOptimisticPlanAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:354
BanditRLProof.FiniteHorizonRL.adaptiveEmpiricalOptimisticRecommendedExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:363
BanditRLProof.FiniteHorizonRL.adaptiveEmpiricalOptimisticOccupancyRadiusSum definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:375
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:395
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_successorPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:421
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.measurableSet_selectedExploratorySimultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:436
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_measurableSet_successorSimultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:471
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_adaptiveSimultaneousCountConfidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:496
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.source_policyAt_succ_eq_adaptiveEmpiricalOptimisticPlanAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:531
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.policyAt_batch_not_mem_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:555
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.SourceCalibration definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:589
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_coordinateConfidenceAt_of_not_mem definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:603
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_optimism_and_recommendedExpectedRegret_of_not_mem theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:652
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_allCoordinateConfidence_optimism_and_recommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticConfidence.lean:710
BanditRLProof.FiniteHorizonRL.MarkovPolicy.occupancySumRemaining_const theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope.lean:33
BanditRLProof.FiniteHorizonRL.adaptiveEmpiricalOptimisticPlanAt_selectedRadiusRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope.lean:57
BanditRLProof.FiniteHorizonRL.adaptiveEmpiricalOptimisticPlanAt_occupancySelectedRadiusRemaining_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope.lean:72
BanditRLProof.FiniteHorizonRL.adaptiveEmpiricalOptimisticOccupancyRadiusSum_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope.lean:103
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_allCoordinateConfidence_optimism_and_explicitRecommendedExpectedRegret_of_pathSupport_episodeThreshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticOccupancyEnvelope.lean:122
BanditRLProof.FiniteHorizonRL.TransitionCountSummary abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:42
BanditRLProof.FiniteHorizonRL.EpisodeBatch.transitionCountSummary definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:48
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_transitionCountSummary theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:56
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.visitCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:75
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.empiricalTransitionPMF definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:81
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.empiricalTransitionKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:123
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.empiricalTransitionKernel_isMarkov theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:131
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.optimisticPlan definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:145
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:162
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.toMarkovPolicy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:168
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.optimisticPolicyTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:180
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.optimisticPolicyTable_toMarkovPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:189
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalOptimisticPolicyTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:201
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_empiricalOptimisticPolicyTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:210
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.iidEpisodeBatchKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:226
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.iidEpisodeBatchKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:237
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.latestBatch definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:259
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.measurable_latestBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:267
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.successorTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:274
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.measurable_successorTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:283
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.source definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:297
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.source_successorPolicy_eq_optimisticPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:320
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.measurableSet_selectedSimultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:338
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.source_measurableSet_successorSimultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:365
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.source_trajectoryMeasure_condDistrib_eq_empiricalOptimisticPolicyBatchLaw theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:387
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.source_trajectoryMeasure_adaptiveSimultaneousCountConfidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEmpiricalOptimisticSource.lean:419
BanditRLProof.FiniteHorizonRL.EpisodeBatchPrefix abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:51
BanditRLProof.FiniteHorizonRL.EpisodeBatchTrajectory abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:55
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:67
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:92
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_map_eval_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:113
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_prefix_compProd theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:131
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_condDistrib theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:153
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_condDistrib_eq_iidEpisodeBatchMeasure theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:176
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.initialBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:202
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:209
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.roundBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:218
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.finiteHorizonBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:228
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurableSet_roundBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:241
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurableSet_finiteHorizonBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:260
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_initialBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:282
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_successorBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:298
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_roundBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:336
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_finiteHorizonBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:374
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_conditionalLaw_and_finiteHorizonBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:415
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.initialSimultaneousCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:455
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorSimultaneousCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:466
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.adaptiveSimultaneousCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:480
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.policyAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:491
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.initialSimultaneousCountBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:503
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.successorSimultaneousCountBadEvent_fiber_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:530
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.measurableSet_adaptiveSimultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:563
BanditRLProof.FiniteHorizonRL.AdaptiveEpisodeBatchSource.trajectoryMeasure_adaptiveSimultaneousCountConfidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveEpisodeBatchLaw Compiled BanditRLProof/RL/FiniteHorizonAdaptiveEpisodeBatchLaw.lean:584
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurable_realizedSuccessorCumulativeRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:38
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurable_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:55
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorExpectedCumulativeRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:68
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorExpectedAverageRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:82
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.abs_realizedSuccessorAverageRegret_le_of_expected_le_of_deviation_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:100
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_projectedCumulativeInverseSqrtPathSupport_optimism_and_decayingExplorationAverageAbsoluteRealizedBehaviorConsistency_of_standardBorel theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:141
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.DecayingExplorationStochasticWindowSpace abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:276
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticWindowSource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:283
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticWindowMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:305
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticCommonMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:330
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticCommonMeasure_map_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:354
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticRealizedBehaviorRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:368
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.measurable_decayingExplorationStochasticRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:381
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticCommonBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:399
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticCommonMeasure_badEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:429
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.abs_decayingExplorationStochasticRealizedBehaviorRegretProcess_le_of_not_mem_badEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:490
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_decayingExplorationStochasticCommonMeasure_marginals_and_realizedBehaviorRegret_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceConsistency.lean:527
BanditRLProof.FiniteHorizonRL.MarkovPolicy.expectedRegret_le_two_mul_horizon_of_rewardBound theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorExpectedAverageRegret_le_two_mul_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:79
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_cumulativeSuccessorGlobalReturnDeviation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:113
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.integrable_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:162
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.normalizedSuccessorGlobalReturnMGFFirstMomentBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:229
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.normalizedSuccessorGlobalReturnMGFFirstMomentBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:243
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.normalizedSuccessorGlobalReturnMGFFirstMomentBound_le_confidenceRadius theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:258
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.one_half_le_log_two_div_vanishingAverageConfidenceDelta theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:308
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationNormalizedSuccessorGlobalReturnMGFFirstMomentBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:333
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticCumulativeReturnDeviationProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:374
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticCumulativeReturnDeviationProcess_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:387
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.integrable_decayingExplorationStochasticRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:439
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticCommonCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:481
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.measurableSet_decayingExplorationStochasticCommonCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:505
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticCommonMeasure_countBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:531
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticExpectedAbsoluteRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:567
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticExpectedAbsoluteRealizedBehaviorRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:584
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticExpectedAbsoluteRealizedBehaviorRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:598
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticExpectedAbsoluteRealizedBehaviorRegretBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:610
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticExpectedAbsoluteRealizedBehaviorRegret_le_bound theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:644
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticExpectedAbsoluteRealizedBehaviorRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:850
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_decayingExplorationStochasticCommonMeasure_integrable_expectedAbsoluteRealizedBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:880
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.memLp_one_decayingExplorationStochasticRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:933
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.eLpNorm_one_decayingExplorationStochasticRealizedBehaviorRegretProcess_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:956
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.eLpNorm_one_decayingExplorationStochasticRealizedBehaviorRegretProcess_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:984
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.eLpNorm_one_decayingExplorationStochasticRealizedBehaviorRegretProcess_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:1018
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticRealizedBehaviorRegretLp definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:1052
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticRealizedBehaviorRegretLp_coeFn_ae_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:1073
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationStochasticRealizedBehaviorRegretLp_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:1097
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_decayingExplorationStochasticCommonMeasure_memLp_eLpNorm_L1_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationCommonSpaceL1Consistency.lean:1143
BanditRLProof.FiniteHorizonRL.MDP.globalReturnDeviationPerEpisodeVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:36
BanditRLProof.FiniteHorizonRL.MDP.iidGlobalSampledCumulativeReturnDeviationVarianceProxy_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:46
BanditRLProof.FiniteHorizonRL.MDP.globalReturnDeviationPerEpisodeVarianceProxy_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:67
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnVarianceProxy_coe theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:89
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnConfidenceRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:103
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnConfidenceRadius_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:114
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnConfidenceRadius_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:128
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationStochasticReturnRadiusEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:187
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnConfidenceRadius_le_decayingEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:198
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationStochasticReturnRadiusEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:287
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationNormalizedSuccessorGlobalReturnRadius_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:312
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationStochasticAverageRealizedBehaviorRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:342
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationStochasticRealizedFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:355
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationStochasticAverageRealizedBehaviorRegretBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:360
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationStochasticAverageRealizedBehaviorRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:383
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationStochasticRealizedFailureBudget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:399
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationStochasticRealizedFailureAndRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:406
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:429
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_initialPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:483
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_successorPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:499
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_initialBatch_map_knownRewardEpisodeBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:519
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_batchKernel_map_knownRewardEpisodeBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:544
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_map_projectedPrefix_next_eq_compProd theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:584
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_condDistrib_projectedNext theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:694
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_map_knownRewardEpisodeBatchTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:738
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.projectedAdaptiveCumulativeCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:827
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_successorExpectedCumulativeRegret_eq_projected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:869
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_successorExpectedAverageRegret_eq_projected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:896
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_projectedCumulativeInverseSqrtPathSupport_optimism_and_decayingExplorationAverageExploratoryBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:920
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.decayingExplorationAverageRealizedBehaviorRegretViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:1032
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_projectedCumulativeInverseSqrtPathSupport_optimism_and_decayingExplorationAverageRealizedBehaviorConsistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:1065
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_projectedCumulativeInverseSqrtPathSupport_decayingExplorationAverageRealizedBehaviorConsistency_allWindows theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationConsistency.lean:1259
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_projectedCumulativeInverseSqrtPathSupport_optimism_and_decayingExplorationAverageRealizedBehaviorConsistency_of_standardBorel theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationRegularityClosedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationRegularityClosedConsistency.lean:38
BanditRLProof.FiniteHorizonRL.AdaptiveCumulativeStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_projectedCumulativeInverseSqrtPathSupport_decayingExplorationAverageRealizedBehaviorConsistency_allWindows_of_standardBorel theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationRegularityClosedConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardCumulativeDecayingExplorationRegularityClosedConsistency.lean:105
BanditRLProof.FiniteHorizonRL.ProbabilityTheory.measure_compProd_map_prodMap_of_map_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:35
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.knownRewardEpisodeBatch definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:89
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_knownRewardEpisodeBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:98
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.knownRewardEpisodeBatchPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:103
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_knownRewardEpisodeBatchPrefix theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:111
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.knownRewardEpisodeBatchTrajectory definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:119
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_knownRewardEpisodeBatchTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:127
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.knownRewardEpisodeBatchPrefix_frestrictLe theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:139
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryIIDStochasticEpisodeBatchKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:150
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryIIDStochasticEpisodeBatchKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:165
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.measurable_selectedExploratorySampledReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:202
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:238
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_initialPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:291
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_successorPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:308
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_initialBatch_map_knownRewardEpisodeBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:329
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_batchKernel_map_knownRewardEpisodeBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:354
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_map_projectedPrefix_next_eq_compProd theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:396
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_condDistrib_projectedNext theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:504
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_map_knownRewardEpisodeBatchTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:550
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.projectedAdaptiveSimultaneousCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:640
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_projectedAllCoordinateConfidence_optimism_and_recommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticProjection.lean:660
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_expected_to_realized_successor_average_regret_transport_two_delta theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret.lean:45
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.projectedExploratoryBehaviorExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret.lean:158
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.projectedAverageExploratoryBehaviorExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret.lean:171
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.projectedExploratoryBehaviorExpectedRegret_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret.lean:184
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.projectedAverageExploratoryBehaviorExpectedRegret_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret.lean:232
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.measurable_selectedExploratoryGlobalReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret.lean:271
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_successorExpectedCumulativeRegret_eq_projected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret.lean:330
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_successorExpectedAverageRegret_eq_projected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret.lean:357
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_projectedAllCoordinateConfidence_optimism_and_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardEmpiricalOptimisticRealizedBehaviorRegret.lean:382
BanditRLProof.FiniteHorizonRL.MDP.initialPolicyValueDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:29
BanditRLProof.FiniteHorizonRL.MDP.measurable_initialPolicyValueDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:36
BanditRLProof.FiniteHorizonRL.MDP.initialPolicyValueVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:44
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryMeasure_map_fst theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:55
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryMeasure_initialPolicyValueDeviation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:65
BanditRLProof.FiniteHorizonRL.MDP.initialPolicyValueDeviationAtEpisode definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:112
BanditRLProof.FiniteHorizonRL.MDP.measurable_initialPolicyValueDeviationAtEpisode theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:118
BanditRLProof.FiniteHorizonRL.MDP.initialPolicyValueDeviationSum definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:127
BanditRLProof.FiniteHorizonRL.MDP.measurable_initialPolicyValueDeviationSum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:135
BanditRLProof.FiniteHorizonRL.MDP.iidInitialPolicyValueDeviationVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:145
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeRewardSum definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:151
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeRewardSum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:158
BanditRLProof.FiniteHorizonRL.MDP.globalSampledCumulativeReturnDeviationSum definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:169
BanditRLProof.FiniteHorizonRL.MDP.globalSampledCumulativeReturnDeviationSum_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:178
BanditRLProof.FiniteHorizonRL.MDP.measurable_globalSampledCumulativeReturnDeviationSum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:200
BanditRLProof.FiniteHorizonRL.MDP.iidGlobalSampledCumulativeReturnDeviationVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:211
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iIndepFun_initialPolicyValueDeviationAtEpisode theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:223
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.initialPolicyValueDeviationAtEpisode_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:238
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_initialPolicyValueDeviationSum_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:266
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_globalSampledCumulativeReturnDeviationSum_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:291
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.GlobalReturnMeasurability typeclass Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:325
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:338
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurable_successorGlobalReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:348
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviationKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:357
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviationKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:378
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviationAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:412
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurable_successorGlobalReturnDeviationAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:420
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_condDistrib_successorGlobalReturnDeviationAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:430
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.condExpKernel_map_successorGlobalReturnDeviationAt_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:455
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnPrefixIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:485
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurable_successorGlobalReturnPrefixIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:498
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:517
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnIncrement_stronglyAdapted_piLE theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:526
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnIncrement_succ_hasCondSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:540
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:648
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnVarianceProxy_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:658
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:670
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_cumulativeSuccessorGlobalReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:679
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorPolicyAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:740
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.optimalInitialExpectedReturn definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:749
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorExpectedCumulativeRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:756
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorExpectedAverageRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:766
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.realizedSuccessorCumulativeRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:775
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.realizedSuccessorAverageRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:787
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnIncrement_succ_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:797
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnDeviation_eq_fin_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:816
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.realizedSuccessorCumulativeRegret_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:836
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.realizedSuccessorAverageRegret_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:875
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviationBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:894
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurable_cumulativeSuccessorGlobalReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:906
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurableSet_successorGlobalReturnDeviationBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:917
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_successorGlobalReturnDeviationBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:929
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_expected_to_realized_successor_average_regret_transport theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardRealizedBehaviorRegret.lean:959
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.policyAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:31
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.initialBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:41
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:48
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.roundBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:57
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.finiteHorizonBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:68
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurableSet_finiteHorizonBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:82
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_initialBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:106
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_successorBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:123
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.initialAllCoordinateEmpiricalModelBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:160
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorAllCoordinateEmpiricalModelBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:173
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.adaptiveAllCoordinateEmpiricalModelBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:188
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.multiBatchLocalDelta_pos_of_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:202
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.multiBatchLocalDelta_le_one_of_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:209
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurableSet_initialAllCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:220
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurableSet_adaptiveAllCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:234
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.initialAllCoordinateEmpiricalModelBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:251
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorAllCoordinateEmpiricalModelBadEvent_fiber_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:280
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.ofReal_multiBatchLocalDelta_add theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:319
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_adaptiveAllCoordinateEmpiricalModelBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:348
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.policyAt_batch_not_mem_allCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:425
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selectedExploratoryStochasticAllCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:466
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_measurableSet_successorAllCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:521
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_adaptiveAllCoordinateEmpiricalModelBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:557
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_finiteRound_allCoordinateConfidence_optimism_and_recommendedExpectedRegret_of_pathSupport_explicitCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticConfidence.lean:608
BanditRLProof.FiniteHorizonRL.StochasticEpisodeBatch.sampledEmpiricalOptimisticPolicyTable_toMarkovPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret.lean:32
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticSuccessorExploratoryBehaviorExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret.lean:49
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_successorPolicy_frestrictLe_eq_sampledPlanExploratoryPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret.lean:65
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_cumulativeSuccessorPolicyExpectedRegret_eq_sampledPlanExploratoryBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret.lean:83
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticSuccessorExploratoryBehaviorExpectedRegret_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret.lean:111
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimistic_optimism_and_cumulativeSuccessorExploratoryBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret.lean:167
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_finiteRound_allCoordinateConfidence_optimism_and_cumulativeSuccessorExploratoryBehaviorExpectedRegret_of_pathSupport_explicitCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeExploratoryBehaviorRegret.lean:229
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticPlanAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret.lean:27
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticRecommendedExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret.lean:38
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticOccupancyRadiusSum definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret.lean:51
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimistic_optimism_and_cumulativeRecommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret.lean:68
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_finiteRound_allCoordinateConfidence_optimism_and_cumulativeRecommendedExpectedRegret_of_pathSupport_explicitCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticCumulativeRecommendedRegret.lean:110
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticPlanAt_selectedRadiusRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret.lean:29
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticPlanAt_occupancySelectedRadiusRemaining_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret.lean:46
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticOccupancyRadiusSum_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret.lean:77
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticExplicitBudgetAverageBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret.lean:93
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimistic_occupancyAndChargeAverage_eq_explicitBudgetAverageBound theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret.lean:102
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_finiteRound_allCoordinateConfidence_optimism_and_explicitBudgetRealizedSuccessorAverageRegret_of_pathSupport_explicitCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticExplicitBudgetRealizedBehaviorRegret.lean:132
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_successorExpectedCumulativeRegret_eq_sampledPlanExploratoryBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticRealizedBehaviorRegret.lean:51
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_successorExpectedAverageRegret_eq_sampledPlanExploratoryBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticRealizedBehaviorRegret.lean:75
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_finiteRound_allCoordinateConfidence_optimism_and_realizedSuccessorAverageRegret_of_pathSupport_explicitCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticRealizedBehaviorRegret.lean:99
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_successorPolicyAt_expectedRegret_le_rateAt_of_not_mem_modelRoundBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency.lean:50
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalSuccessorPolicyExpectedRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency.lean:152
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalSuccessorPolicyExpectedRegretProcess_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency.lean:169
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_successorPolicyExpectedRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency.lean:194
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_eventually_modelOptimistic_and_behaviorExpected_and_realizedRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureBehaviorExpectedRegretConsistency.lean:257
BanditRLProof.summable_exp_neg_sqrt_natCast theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:20
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.natCast_le_successorEpisodeMass theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:83
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.summable_exp_neg_sqrt_successorEpisodeMass theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:96
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_selfConsistentScheduledCausalVanishingReturnDelta theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:116
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_selfConsistentScheduledCausalVanishingReturnFailureBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:135
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalVanishingReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:145
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledCausalVanishingReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:162
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_vanishingReturnBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:186
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_selfConsistentScheduledCausalModelRoundBadEvent_measure_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:255
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_selfConsistentScheduledCausalVanishingReturnBadEvent_measure_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:278
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_eventually_not_mem_selfConsistentScheduledCausalModel_and_returnBadEvents theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:309
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_eventually_abs_selfConsistentScheduledNaturalCausalRealizedRegret_le_envelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:356
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_realizedRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:431
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_eventually_modelOptimistic_and_realizedRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceAlmostSureConsistency.lean:492
BanditRLProof.FiniteHorizonRL.integral_le_add_const_mul_measureReal_of_le_on_compl theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:38
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalPlanningRateAt_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:84
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalCoordinateModelFailureBudget_toReal_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:96
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalIntegratedBehaviorExpectedRegretRateAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:112
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalIntegratedBehaviorExpectedRegretRateAt_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:123
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalIntegratedBehaviorExpectedRegretRateAt_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:146
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteBehaviorRegret_le_rateAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:156
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalIntegratedBehaviorExpectedRegretRateAt_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:249
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteBehaviorRegret_tendsto_zero_of_explicit_rate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:264
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_behaviorExpectedRegret_explicitIntegratedRate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretExplicitIntegratedRate.lean:295
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:51
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedCumulativeBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:65
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeIntegratedBehaviorExpectedRegretRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:80
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:87
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageIntegratedBehaviorExpectedRegretRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:100
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretProcess_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:106
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:123
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedCumulativeBehaviorRegret_eq_sum_expectedAbsolute theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:144
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedCumulativeBehaviorRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:178
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeIntegratedBehaviorExpectedRegretRate_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:197
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedCumulativeBehaviorRegret_le_rate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:206
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegret_le_rate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:236
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageIntegratedBehaviorExpectedRegretRate_eq_natWeightedAverage theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:268
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageIntegratedBehaviorExpectedRegretRate_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:282
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:300
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:317
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_cumulative_and_averageBehaviorExpectedRegret_explicitRate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretFinitePrefixCumulativeAverageRate.lean:350
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.measurable_exploratoryPolicy_expectedRegret_comp theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretInMeasureConsistency.lean:47
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalSuccessorPolicyExpectedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretInMeasureConsistency.lean:81
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_successorPolicyExpectedRegret_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretInMeasureConsistency.lean:121
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_behaviorExpected_and_realizedRegret_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretInMeasureConsistency.lean:166
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalSuccessorPolicyExpectedRegretProcess_le_two_mul_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:50
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalSuccessorPolicyExpectedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:72
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:103
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:119
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalSuccessorPolicyExpectedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:193
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalSuccessorPolicyExpectedRegretProcess_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:216
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalSuccessorPolicyExpectedRegretProcess_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:244
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalSuccessorPolicyExpectedRegretProcess_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:279
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBehaviorExpectedRegretLp definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:314
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBehaviorExpectedRegretLp_coeFn_ae_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:334
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBehaviorExpectedRegretLp_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:361
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_behaviorExpectedRegret_memLp_eLpNorm_L1_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:408
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_behaviorExpected_and_realizedRegret_L1_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceBehaviorExpectedRegretL1Consistency.lean:479
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_realizedSuccessorCumulativeRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:51
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:69
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorWeightedExpectedCumulativeRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:82
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorWeightedExpectedAverageRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:98
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.abs_realizedSuccessorAverageRegret_le_of_expected_le_of_deviation_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:119
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledLocalDelta_eq_inv_pow theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:162
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_selfConsistentScheduledLocalDelta theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:181
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalCoordinateModelFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:199
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalTailModelFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:209
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_selfConsistentScheduledCausalCoordinateModelFailureBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:218
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalTailModelFailureBudget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:242
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalModelRoundBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:252
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalTailModelBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:274
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledCausalModelRoundBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:290
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledCausalTailModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:333
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_modelRoundBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:350
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_tailModelBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:433
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.not_mem_selfConsistentScheduledCausalModelRoundBadEvent_of_not_mem_tail theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:473
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_coordinateConfidence_of_not_mem_modelRoundBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:502
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalLocalPlanningBound_le_rateAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:670
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalBurninExpectedRegretRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:707
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalBurninExpectedRegretRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:725
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_weightedExpectedSuccessorAverageRegret_le_burninEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:759
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalVanishingReturnDelta definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:988
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalVanishingReturnDelta_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1002
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalVanishingReturnDelta_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1013
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalVanishingReturnDelta_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1026
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalVanishingReturnRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1069
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.normalizedSuccessorGlobalReturnConfidenceRadius_vanishingDelta_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1089
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalVanishingReturnRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1158
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalTailModelReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1198
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalTailModelReturnFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1218
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalBurninRealizedRegretRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1227
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalBurninRealizedRegretRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1239
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_tail_optimism_and_absoluteRealizedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1258
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRealizedRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1462
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalRealizedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1478
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_realizedRegret_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceConsistency.lean:1501
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorWeightedExpectedAverageRegret_le_two_mul_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:45
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_cumulativeSuccessorGlobalReturnDeviation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:94
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.integrable_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:149
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnMGFFirstMomentBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:216
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnMGFFirstMomentBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:230
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnMGFFirstMomentBound_le_confidenceRadius theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:244
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalTailModelFailureBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:298
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalTailModelFailureBudget_toReal_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:317
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalNormalizedReturnMGFFirstMomentBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:328
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalNormalizedReturnMGFFirstMomentBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:341
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalNormalizedReturnMGFFirstMomentBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:353
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalBurninExpectedRegretRateEnvelope_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:421
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteRealizedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:452
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalBurninExpectedAbsoluteRegretL1Envelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:467
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalBurninExpectedAbsoluteRegretL1Envelope_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:481
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalRealizedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:496
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteRealizedRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:547
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteRealizedRegret_le_burninL1Envelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:566
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteRealizedRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:755
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalRealizedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:860
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalRealizedRegretProcess_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:884
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalRealizedRegretProcess_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:914
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalRealizedRegretProcess_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:949
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRealizedRegretLp definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:984
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRealizedRegretLp_coeFn_ae_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:1005
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRealizedRegretLp_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:1034
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_naturalRealizedRegret_memLp_eLpNorm_L1_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalCommonSpaceL1Consistency.lean:1084
BanditRLProof.natWeightedAverage definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:27
BanditRLProof.tendsto_natWeightedAverage_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:33
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorEpisodeMass_eq_sum_range theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:80
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorEpisodeMass_tendsto_atTop theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:93
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnVarianceProxy_coe theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:110
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnConfidenceRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:127
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnConfidenceRadius_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:139
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.fixedHalfSuccessorGlobalReturnRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:198
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.normalizedSuccessorGlobalReturnConfidenceRadius_half_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:210
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.fixedHalfSuccessorGlobalReturnRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:227
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalPlanningRateAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:250
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalPlanningRateAt_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:264
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalWeightedPlanningRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:302
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSuccessorPlanningAverageBound_le_rateEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:311
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalWeightedPlanningRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:392
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalReturnRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:406
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalReturnRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:419
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalRealizedSuccessorAverageRegretRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:434
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalRealizedSuccessorAverageRegretRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:446
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_optimism_and_realizedSuccessorAverageRegret_le_explicitRateEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalExplicitRate.lean:465
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.policyAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:49
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.initialBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:60
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:67
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.roundBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:76
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.finiteHorizonBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:87
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurableSet_finiteHorizonBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:101
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_initialBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:125
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_successorBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:143
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.initialAllCoordinateEmpiricalModelBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:180
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorAllCoordinateEmpiricalModelBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:192
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.adaptiveAllCoordinateEmpiricalModelBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:206
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.cumulativeModelFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:220
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurableSet_initialAllCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:226
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurableSet_adaptiveAllCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:240
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.initialAllCoordinateEmpiricalModelBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:257
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorAllCoordinateEmpiricalModelBadEvent_fiber_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:282
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_adaptiveAllCoordinateEmpiricalModelBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:323
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.policyAt_batch_not_mem_allCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:403
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.heterogeneousExploratorySource_measurableSet_successorAllCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:442
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.heterogeneousExploratorySource_trajectoryMeasure_adaptiveAllCoordinateEmpiricalModelBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:477
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalModelFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:526
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalModelBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:534
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_allCoordinateConfidence_optimism_and_recommendedExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalModelConfidence.lean:556
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorPolicyAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:56
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorEpisodeMass definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:66
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorEpisodeMass_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:73
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorWeightedExpectedCumulativeRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:85
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorWeightedExpectedAverageRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:97
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.realizedSuccessorCumulativeRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:108
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.realizedSuccessorAverageRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:124
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnIncrement_succ_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:138
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnDeviation_eq_fin_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:163
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.realizedSuccessorCumulativeRegret_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:188
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.realizedSuccessorAverageRegret_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:235
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviationBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:254
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_cumulativeSuccessorGlobalReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:271
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurableSet_successorGlobalReturnDeviationBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:286
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_successorGlobalReturnDeviationBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:300
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_weightedExpected_to_realized_successor_average_regret_transport theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:340
BanditRLProof.FiniteHorizonRL.MDP.stochasticAllCoordinateEmpiricalFiniteBatchModel_occupancySelectedRadiusRemaining_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:458
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.heterogeneousExploratorySource_successorPolicyAt_eq_sampledPlanExploratoryPolicy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:491
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.heterogeneousExploratorySource_successorPolicyAt_expectedRegret_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:511
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSuccessorPlanningCumulativeBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:550
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSuccessorPlanningAverageBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:571
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_optimism_and_weightedExpectedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:587
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSuccessorReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:754
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalModelReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:771
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalModelReturnFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:789
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_optimism_and_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalRealizedSuccessorRegret.lean:800
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorSampledReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:54
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorDeviationKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:65
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorDeviationKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:88
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorSampledReturnDeviationAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:124
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_successorSampledReturnDeviationAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:137
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_condDistrib_successorSampledReturnDeviationAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:151
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.condExpKernel_map_successorSampledReturnDeviationAt_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:183
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationPrefixIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:220
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_sampledReturnDeviationPrefixIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:240
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:263
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_sampledReturnDeviationIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:276
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationIncrement_stronglyAdapted_piLE theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:288
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationIncrement_zero_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:306
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationIncrement_succ_hasCondSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:339
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.cumulativeSampledReturnDeviationVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:457
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.cumulativeSampledReturnDeviationVarianceProxy_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:468
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.cumulativeSampledReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:502
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_cumulativeSampledReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:515
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.GlobalReturnMeasurability typeclass Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:577
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:591
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_successorGlobalReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:604
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviationKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:613
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviationKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:636
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnDeviationAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:675
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_successorGlobalReturnDeviationAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:688
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_condDistrib_successorGlobalReturnDeviationAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:702
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.condExpKernel_map_successorGlobalReturnDeviationAt_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:733
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnPrefixIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:769
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_successorGlobalReturnPrefixIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:787
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:808
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnIncrement_stronglyAdapted_piLE theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:821
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.successorGlobalReturnIncrement_succ_hasCondSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:838
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:957
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnVarianceProxy_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:971
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.cumulativeSuccessorGlobalReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:1016
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_cumulativeSuccessorGlobalReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:1029
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_cumulativeSampledReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:1119
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_cumulativeSuccessorGlobalReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalReturnConcentration.lean:1166
BanditRLProof.FiniteHorizonRL.HeterogeneousStochasticEpisodeBatchTrajectory abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:53
BanditRLProof.FiniteHorizonRL.HeterogeneousStochasticEpisodeBatchPrefix abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:58
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:66
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:99
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_map_eval_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:124
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_prefix_compProd theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:143
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_condDistrib_nextBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:164
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_map_prefix_projective theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:189
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.heterogeneousLatestBatch definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:209
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_heterogeneousLatestBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:218
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.heterogeneousSuccessorTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:228
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_heterogeneousSuccessorTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:237
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.heterogeneousExploratorySource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:252
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:292
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_exactLaws_and_projective theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCausalSource.lean:323
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_selfConsistentScheduledExplicitRate_allCoordinateConfidence_optimism_and_absoluteRealizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:67
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.SelfConsistentScheduledStochasticWindowSpace abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:290
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledStochasticWindowSource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:298
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledStochasticWindowMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:320
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledStochasticCommonMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:347
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledStochasticCommonMeasure_map_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:374
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledStochasticRealizedRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:390
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledStochasticRealizedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:405
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledStochasticCommonBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:424
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledStochasticCommonMeasure_badEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:444
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.abs_selfConsistentScheduledStochasticRealizedRegretProcess_le_of_not_mem_badEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:497
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_selfConsistentScheduledStochasticCommonMeasure_marginals_and_realizedRegret_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentCommonSpaceConsistency.lean:536
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionBudgetRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:44
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionBudgetRateEnvelope_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:52
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionBudget_le_rateEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:62
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledPlanningAverageRegretRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:127
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledPlanningAverageRegretBound_le_rateEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:137
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedSuccessorAverageRegretRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:171
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedSuccessorAverageRegretBound_le_rateEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:177
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedFailureRateEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:196
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedFailureBudget_eq_rateEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:207
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledPlanningAverageRegretRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:226
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedSuccessorAverageRegretRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:257
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedFailureRateEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:275
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledExplicitRateEnvelopes_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:288
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_selfConsistentScheduledExplicitRate_allCoordinateConfidence_optimism_and_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentExplicitRate.lean:312
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_finiteRound_allCoordinateConfidence_optimism_and_recommendedExpectedRegret_of_pathSupport_selfConsistentCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret.lean:39
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_finiteRound_allCoordinateConfidence_optimism_and_cumulativeSuccessorExploratoryBehaviorExpectedRegret_of_pathSupport_selfConsistentCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret.lean:190
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimisticSelfConsistentBudgetAverageBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret.lean:304
BanditRLProof.FiniteHorizonRL.adaptiveStochasticSampledEmpiricalOptimistic_occupancyAndChargeAverage_eq_selfConsistentBudgetAverageBound theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret.lean:316
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_finiteRound_allCoordinateConfidence_optimism_and_selfConsistentBudgetRealizedSuccessorAverageRegret_of_pathSupport_selfConsistentCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentRealizedBehaviorRegret.lean:346
BanditRLProof.FiniteHorizonRL.selfConsistentCountShrinkEpisodeThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:31
BanditRLProof.FiniteHorizonRL.selfConsistentRewardShrinkEpisodeThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:39
BanditRLProof.FiniteHorizonRL.simultaneousCountConfidenceRadius_lt_episodes_mul_visitFloor_div_scale_sq_of_threshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:52
BanditRLProof.FiniteHorizonRL.simultaneousRewardSumConfidenceRadius_lt_episodes_mul_visitFloor_div_two_scale_sq_of_threshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:117
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledEpisodeThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:193
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledEpisodes definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:218
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledEpisodes_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:227
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledEpisodeThreshold_lt_episodes theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:237
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.exploratoryPathCalibrationEpisodeThreshold_lt_selfConsistentScheduledEpisodes theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:254
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentCountShrinkEpisodeThreshold_lt_scheduledEpisodes theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:269
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentRewardShrinkEpisodeThreshold_lt_scheduledEpisodes theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:284
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduled_countMargin_and_halfContraction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:301
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledLocalDelta definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:333
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRewardBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:340
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionContraction definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:351
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:361
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledCountRadius_lt_mass_div_scale_sq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:372
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRewardSumRadius_lt_mass_div_two_scale_sq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:398
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionContractionEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:424
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRewardBudget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:430
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRewardBudget_lt_inv_scale_sq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:441
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionContraction_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:499
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionContraction_lt_envelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:511
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionContraction_lt_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:586
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionBudget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:601
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.decayingExplorationScale_sq_tendsto_atTop theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:621
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionContractionEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:638
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRewardBudget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:646
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionContraction_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:664
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledTransitionBudget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:683
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledPlanningAverageRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:719
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedSuccessorAverageRegretBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:731
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:743
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledPlanningAverageRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:749
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledNormalizedSuccessorGlobalReturnRadius_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:784
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedSuccessorAverageRegretBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:806
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledRealizedFailureBudget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:825
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.selfConsistentScheduledFailureAndRealizedBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:834
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_selfConsistentScheduled_allCoordinateConfidence_optimism_and_realizedSuccessorAverageRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSelfConsistentSchedule.lean:858
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_rewardSum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:38
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_empiricalReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:62
BanditRLProof.FiniteHorizonRL.TransitionCountSummary.stateKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:76
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionStateKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:102
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionStateKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:122
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_uncurry_of_forall_measurable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:140
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurable_empiricalTransitionValue theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:163
BanditRLProof.FiniteHorizonRL.MDP.measurable_stochasticAllCoordinateEmpiricalOptimisticQ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:187
BanditRLProof.FiniteHorizonRL.MDP.measurable_stochasticAllCoordinateEmpiricalUpperValueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:209
BanditRLProof.FiniteHorizonRL.MDP.measurable_stochasticAllCoordinateEmpiricalOptimisticActionAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:256
BanditRLProof.FiniteHorizonRL.MDP.measurable_stochasticAllCoordinateEmpiricalOptimisticPolicyTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:291
BanditRLProof.FiniteHorizonRL.StochasticEpisodeBatch.sampledEmpiricalOptimisticPolicyTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:309
BanditRLProof.FiniteHorizonRL.StochasticEpisodeBatch.measurable_sampledEmpiricalOptimisticPolicyTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:320
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.latestBatch definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:336
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_latestBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:345
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.successorTable definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:354
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_successorTable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:362
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:374
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exploratorySource_batchKernel_eq_selectedPolicy_iidLaw theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardSampledEmpiricalOptimisticSource.lean:408
ProbabilityTheory.Kernel.retainedInputKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:31
ProbabilityTheory.Kernel.retainedInputKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:43
ProbabilityTheory.Kernel.condDistrib_pair_ae_eq_retainedInputKernel_of_pair_map_eq_compProd theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:53
ProbabilityTheory.Kernel.condDistrib_dynamic_map_ae_eq_of_pair_map_eq_compProd theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:115
BanditRLProof.FiniteHorizonRL.StochasticEpisodeBatch abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:168
BanditRLProof.FiniteHorizonRL.StochasticEpisodeBatchPrefix abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:173
BanditRLProof.FiniteHorizonRL.StochasticEpisodeBatchTrajectory abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:178
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:189
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:224
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_map_eval_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:244
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_prefix_compProd theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:259
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorSampledReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:278
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorDeviationKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:289
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorDeviationKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:310
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.successorSampledReturnDeviationAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:343
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurable_successorSampledReturnDeviationAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:351
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_condDistrib_successorSampledReturnDeviationAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:361
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.condExpKernel_map_successorSampledReturnDeviationAt_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:387
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationPrefixIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:417
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurable_sampledReturnDeviationPrefixIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:432
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:455
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.measurable_sampledReturnDeviationIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:464
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationIncrement_stronglyAdapted_piLE theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:473
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationIncrement_zero_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:487
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.sampledReturnDeviationIncrement_succ_hasCondSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:520
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.cumulativeSampledReturnDeviationVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:626
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.cumulativeSampledReturnDeviationVarianceProxy_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:633
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.cumulativeSampledReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:644
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_cumulativeSampledReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonAdaptiveStochasticRewardTotalReturnConcentration.lean:654
BanditRLProof.FiniteHorizonRL.abs_integral_sub_integral_le_sum_coordinateRadius_mul_envelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonCoordinateModelConfidence Compiled BanditRLProof/RL/FiniteHorizonCoordinateModelConfidence.lean:29
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.CoordinateConfidence structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonCoordinateModelConfidence Compiled BanditRLProof/RL/FiniteHorizonCoordinateModelConfidence.lean:81
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.CoordinateConfidence.transitionError_le_radius theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonCoordinateModelConfidence Compiled BanditRLProof/RL/FiniteHorizonCoordinateModelConfidence.lean:116
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.CoordinateConfidence.toConfidence definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonCoordinateModelConfidence Compiled BanditRLProof/RL/FiniteHorizonCoordinateModelConfidence.lean:144
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.CoordinateConfidence.optimism_and_expectedRegret_le_two_occupancySelectedRadiusRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonCoordinateModelConfidence Compiled BanditRLProof/RL/FiniteHorizonCoordinateModelConfidence.lean:154
BanditRLProof.FiniteHorizonRL.EpisodeStep structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:31
BanditRLProof.FiniteHorizonRL.EpisodeStep.measurable_state theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:49
BanditRLProof.FiniteHorizonRL.EpisodeStep.measurable_action theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:60
BanditRLProof.FiniteHorizonRL.EpisodeStep.measurable_reward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:71
BanditRLProof.FiniteHorizonRL.EpisodeStep.measurable_nextState theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:82
BanditRLProof.FiniteHorizonRL.EpisodeBatch abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:97
BanditRLProof.FiniteHorizonRL.EpisodeBatch.visitCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:103
BanditRLProof.FiniteHorizonRL.EpisodeBatch.rewardSum definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:110
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalReward definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:118
BanditRLProof.FiniteHorizonRL.EpisodeBatch.transitionCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:125
BanditRLProof.FiniteHorizonRL.EpisodeBatch.sum_transitionCount_eq_visitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:135
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionPMF definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:153
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionMass definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:194
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionPMF_eq_pure_of_visitCount_eq_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:204
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionPMF_apply_of_visitCount_ne_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:216
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionMass_eq_div_of_visitCount_ne_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:230
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:245
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:255
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionKernel_isMarkov theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:265
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalTransitionKernel_real_singleton theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:278
BanditRLProof.FiniteHorizonRL.MDP.FiniteBatchModel structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:300
BanditRLProof.FiniteHorizonRL.MDP.FiniteBatchModel.plan definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:309
BanditRLProof.FiniteHorizonRL.MDP.FiniteBatchModel.Confidence structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:327
BanditRLProof.FiniteHorizonRL.MDP.FiniteBatchModel.Confidence.toCoordinateConfidence definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:362
BanditRLProof.FiniteHorizonRL.MDP.FiniteBatchModel.Confidence.optimism_and_expectedRegret_le_two_occupancySelectedRadiusRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEmpiricalModel Compiled BanditRLProof/RL/FiniteHorizonEmpiricalModel.lean:392
BanditRLProof.FiniteHorizonRL.EpisodeStep.toProdEquiv definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEpisodeBatchStandardBorel Compiled BanditRLProof/RL/FiniteHorizonEpisodeBatchStandardBorel.lean:30
BanditRLProof.FiniteHorizonRL.MDP.decisionStageRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:32
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:41
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.exactModelPlan definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:65
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.transitionValue definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:76
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.bellmanQ definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:83
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.optimisticQ definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:91
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.measurable_transitionValue theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:101
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.measurable_optimisticQ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:110
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.optimisticAction definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:122
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.optimisticQ_le_optimisticAction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:130
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.optimisticBellman definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:141
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.measurable_optimisticAction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:148
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.upperValueRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:155
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.upperValueRemaining_eq_of_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:165
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.measurable_upperValueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:175
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.Confidence structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:185
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.exactModelPlan_confidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:203
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.Confidence.trueBellmanQ_le_optimisticQ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:213
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.certificate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:231
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.Confidence.optimalValueRemaining_le_upperValueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:258
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.optimisticActionAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:268
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.measurable_optimisticActionAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:276
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.optimisticPolicy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:283
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.optimisticActionAt_decisionStageRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:296
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.optimisticPolicy_bellman_eq_bellmanQ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:311
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.selectedRadiusRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:324
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.Confidence.selectedRadiusRemaining_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:336
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.Confidence.policyBellmanResidual_le_two_selectedRadiusRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:357
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.Confidence.expectedRegret_le_two_occupancySelectedRadiusRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:392
BanditRLProof.FiniteHorizonRL.MDP.EstimatedModelPlan.Confidence.optimism_and_expectedRegret_le_two_occupancySelectedRadiusRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonEstimatedModelCertificate Compiled BanditRLProof/RL/FiniteHorizonEstimatedModelCertificate.lean:425
BanditRLProof.FiniteHorizonRL.exploratoryPathCalibrationDimensionFactor definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportEpisodeThreshold Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportEpisodeThreshold.lean:28
BanditRLProof.FiniteHorizonRL.one_le_exploratoryPathCalibrationDimensionFactor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportEpisodeThreshold Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportEpisodeThreshold.lean:36
BanditRLProof.FiniteHorizonRL.exploratoryPathCalibrationEpisodeThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportEpisodeThreshold Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportEpisodeThreshold.lean:49
BanditRLProof.FiniteHorizonRL.simultaneousCountConfidenceRadius_lt_episodes_mul_visitFloor_div_dimensionFactor_of_threshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportEpisodeThreshold Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportEpisodeThreshold.lean:64
BanditRLProof.FiniteHorizonRL.episodeThreshold_countMargin_and_halfContraction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportEpisodeThreshold Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportEpisodeThreshold.lean:137
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_sourceTransitionBonusCover_of_pathSupport_episodeThreshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportEpisodeThreshold Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportEpisodeThreshold.lean:195
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_sourceCalibration_of_pathSupport_episodeThreshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportEpisodeThreshold Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportEpisodeThreshold.lean:222
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_allCoordinateConfidence_optimism_and_recommendedExpectedRegret_of_pathSupport_episodeThreshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportEpisodeThreshold Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportEpisodeThreshold.lean:251
BanditRLProof.FiniteHorizonRL.uniformFloorTransitionCoordinateRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:32
BanditRLProof.FiniteHorizonRL.uniformFloorTransitionCoordinateRadius_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:42
BanditRLProof.FiniteHorizonRL.MarkovPolicy.expectedCountTransitionCoordinateRadius_le_uniformFloor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:60
BanditRLProof.FiniteHorizonRL.ExploratoryPathUniformVisitFloor definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:94
BanditRLProof.FiniteHorizonRL.ExploratoryPathUniformVisitFloor.exploratoryStateCountMargin theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:107
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.uniformVisitFloor_expectedCount_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:125
BanditRLProof.FiniteHorizonRL.MarkovPolicy.transitionBonusCover_rewardBound_of_uniformExpectedCountFloor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:164
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_sourceTransitionBonusCover_of_pathSupport_explicitCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:225
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_sourceCalibration_of_pathSupport_explicitCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:270
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_allCoordinateConfidence_optimism_and_recommendedExpectedRegret_of_pathSupport_explicitCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportExplicitCalibration.lean:306
BanditRLProof.FiniteHorizonRL.MDP.trajectoryStateAt_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:34
BanditRLProof.FiniteHorizonRL.MDP.episodeStepOfTrajectory_nextState_eq_trajectoryStateAt_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:44
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageStateProbability_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:59
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageTransitionJointProbability_le_stageStateProbability_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:83
BanditRLProof.FiniteHorizonRL.ExploratoryPathSupport structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:104
BanditRLProof.FiniteHorizonRL.exploratoryPathStateLowerNat definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:121
BanditRLProof.FiniteHorizonRL.exploratoryPathStateLower definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:134
BanditRLProof.FiniteHorizonRL.exploratoryPathStateLowerNat_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:144
BanditRLProof.FiniteHorizonRL.exploratoryPathStateLower_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:169
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryPathStateLower_le_stageStateProbability theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:183
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_sourceStateReachability_of_pathSupport theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:270
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_sourceCalibration_of_pathSupport theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:293
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_allCoordinateConfidence_optimism_and_recommendedExpectedRegret_of_pathSupport theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryPathSupportReachability Compiled BanditRLProof/RL/FiniteHorizonExploratoryPathSupportReachability.lean:327
BanditRLProof.FiniteHorizonRL.exploratoryActionProbabilityFloor definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:28
BanditRLProof.FiniteHorizonRL.exploratoryActionProbabilityFloor_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:36
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageStateProbability_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:48
BanditRLProof.FiniteHorizonRL.MarkovPolicy.TransitionBonusCover definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:57
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryActionProbabilityFloor_le_exploratoryActionPMF_toReal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:81
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryActionProbabilityFloor_le_actionKernel_real theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:97
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.stateLower_mul_exploratoryActionProbabilityFloor_le_stageVisitProbability theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:115
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.stateLower_expectedCount_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:147
BanditRLProof.FiniteHorizonRL.ExploratoryStateCountMargin definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:174
BanditRLProof.FiniteHorizonRL.MarkovPolicy.empiricalOptimisticCalibration_exploratoryPolicy_of_stateReachability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:188
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.SourceStateReachability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:216
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.SourceTransitionBonusCover definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:231
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_sourceCalibration_of_stateReachability theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:248
BanditRLProof.FiniteHorizonRL.AdaptiveEmpiricalOptimisticSource.exploratorySource_trajectoryMeasure_allCoordinateConfidence_optimism_and_recommendedExpectedRegret_of_stateReachability theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonExploratoryReachabilityCalibration Compiled BanditRLProof/RL/FiniteHorizonExploratoryReachabilityCalibration.lean:294
BanditRLProof.FiniteHorizonRL.empiricalFiniteBatchValueEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:30
BanditRLProof.FiniteHorizonRL.MDP.allCoordinateEmpiricalFiniteBatchModel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:40
BanditRLProof.FiniteHorizonRL.MarkovPolicy.expectedCountTransitionCoordinateRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:54
BanditRLProof.FiniteHorizonRL.MarkovPolicy.expectedCount_sub_radius_lt_count_of_not_mem_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:68
BanditRLProof.FiniteHorizonRL.MarkovPolicy.empiricalTransitionMass_abs_sub_transition_le_expectedCountRadius_of_not_mem theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:94
BanditRLProof.FiniteHorizonRL.MarkovPolicy.empiricalReward_eq_of_not_mem_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:140
BanditRLProof.FiniteHorizonRL.MarkovPolicy.AllCoordinateConfidence.upperValueRemaining_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:171
BanditRLProof.FiniteHorizonRL.MarkovPolicy.allCoordinateEmpiricalFiniteBatchModelConfidence_of_not_mem definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:251
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_allCoordinate_finiteBatchModel_confidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:315
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_allCoordinate_optimism_and_expectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDAllCoordinateFiniteBatchConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDAllCoordinateFiniteBatchConfidence.lean:362
BanditRLProof.FiniteHorizonRL.EpisodeStep.visitIndicator definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:32
BanditRLProof.FiniteHorizonRL.EpisodeStep.transitionIndicator definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:37
BanditRLProof.FiniteHorizonRL.EpisodeStep.measurable_visitIndicator theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:44
BanditRLProof.FiniteHorizonRL.EpisodeStep.measurable_transitionIndicator theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:54
BanditRLProof.FiniteHorizonRL.EpisodeStep.visitIndicator_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:68
BanditRLProof.FiniteHorizonRL.EpisodeStep.transitionIndicator_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:78
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageVisitProbability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:91
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageTransitionJointProbability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:104
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageVisitProbability_eq_measureReal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:115
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageTransitionJointProbability_eq_measureReal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:140
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageVisitProbability_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:171
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageTransitionJointProbability_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:181
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageTransitionJointProbability_le_stageVisitProbability theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:194
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integral_visitIndicator_iidEpisodeBatchMeasure_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:209
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integral_transitionIndicator_iidEpisodeBatchMeasure_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:245
BanditRLProof.FiniteHorizonRL.MarkovPolicy.centeredVisitIndicator definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:281
BanditRLProof.FiniteHorizonRL.MarkovPolicy.centeredTransitionIndicator definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:290
BanditRLProof.FiniteHorizonRL.MarkovPolicy.sum_visitIndicator_eq_cast_visitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:302
BanditRLProof.FiniteHorizonRL.MarkovPolicy.sum_transitionIndicator_eq_cast_transitionCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:314
BanditRLProof.FiniteHorizonRL.MarkovPolicy.sum_centeredVisitIndicator_eq_cast_visitCount_sub theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:327
BanditRLProof.FiniteHorizonRL.MarkovPolicy.sum_centeredTransitionIndicator_eq_cast_transitionCount_sub theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:350
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurable_cast_visitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:376
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurable_cast_transitionCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:391
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurable_visitCountDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:408
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurable_transitionCountDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:421
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidBernoulliVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:433
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidBernoulliVarianceProxy_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:437
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidBernoulliVarianceProxy_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:443
BanditRLProof.FiniteHorizonRL.MarkovPolicy.centeredVisitIndicator_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:457
BanditRLProof.FiniteHorizonRL.MarkovPolicy.centeredTransitionIndicator_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:488
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_centeredVisitIndicator theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:522
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_centeredTransitionIndicator theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:538
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurableSet_visitCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:555
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurableSet_transitionCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:572
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_visitCount_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:594
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_transitionCount_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:629
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_visit_and_transition_count_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDCountConcentration Compiled BanditRLProof/RL/FiniteHorizonIIDCountConcentration.lean:667
BanditRLProof.FiniteHorizonRL.MarkovPolicy.empiricalTransitionMass_abs_sub_transition_lt_of_not_mem_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleEmpiricalTransitionConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleEmpiricalTransitionConfidence.lean:36
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_eligible_empiricalTransitionMass_confidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleEmpiricalTransitionConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleEmpiricalTransitionConfidence.lean:125
BanditRLProof.FiniteHorizonRL.VisitCoordinate structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:29
BanditRLProof.FiniteHorizonRL.VisitCoordinate.count definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:38
BanditRLProof.FiniteHorizonRL.VisitCoordinate.expectedCount definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:43
BanditRLProof.FiniteHorizonRL.VisitCoordinate.zeroCountEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:53
BanditRLProof.FiniteHorizonRL.VisitCoordinate.measurableSet_zeroCountEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:60
BanditRLProof.FiniteHorizonRL.eligibleZeroVisitCountEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:77
BanditRLProof.FiniteHorizonRL.measurableSet_eligibleZeroVisitCountEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:85
BanditRLProof.FiniteHorizonRL.visitCoordinate_count_pos_of_not_mem_eligibleZeroVisitCountEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:97
BanditRLProof.FiniteHorizonRL.MarkovPolicy.visitCoordinate_count_pos_of_not_mem_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:119
BanditRLProof.FiniteHorizonRL.MarkovPolicy.eligibleZeroVisitCountEvent_subset_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:154
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_eligibleZeroVisitCountEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:179
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_eligible_visit_count_positivity theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDEligibleVisitCountPositivity Compiled BanditRLProof/RL/FiniteHorizonIIDEligibleVisitCountPositivity.lean:210
BanditRLProof.FiniteHorizonRL.EpisodeBatch.RewardConsistent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:29
BanditRLProof.FiniteHorizonRL.EpisodeBatch.measurableSet_rewardConsistent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:36
BanditRLProof.FiniteHorizonRL.EpisodeBatch.rewardSum_eq_visitCount_mul_reward_of_rewardConsistent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:57
BanditRLProof.FiniteHorizonRL.EpisodeBatch.empiricalReward_eq_reward_of_rewardConsistent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:77
BanditRLProof.FiniteHorizonRL.MDP.episodeBatchOfTrajectories_rewardConsistent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:95
BanditRLProof.FiniteHorizonRL.MDP.episodeBatchOfTrajectories_rewardSum_eq_visitCount_mul_reward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:104
BanditRLProof.FiniteHorizonRL.MDP.episodeBatchOfTrajectories_empiricalReward_eq_reward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:119
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchMeasure_rewardConsistent_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:143
BanditRLProof.FiniteHorizonRL.MarkovPolicy.empiricalReward_eq_and_transition_lt_of_not_mem_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:160
BanditRLProof.FiniteHorizonRL.MarkovPolicy.episodeBatchOfTrajectories_empiricalReward_eq_and_transition_lt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:191
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_eligible_empiricalReward_exact_and_transition_confidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDGeneratedEmpiricalRewardExactness Compiled BanditRLProof/RL/FiniteHorizonIIDGeneratedEmpiricalRewardExactness.lean:223
BanditRLProof.FiniteHorizonRL.multiBatchLocalDelta definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:35
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchFamilyMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:41
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchFamilyMeasure_map_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:51
BanditRLProof.FiniteHorizonRL.MarkovPolicy.multiBatchRoundBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:64
BanditRLProof.FiniteHorizonRL.MarkovPolicy.multiBatchSimultaneousCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:75
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurableSet_multiBatchSimultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:85
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchFamilyMeasure_roundBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:100
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchFamilyMeasure_multiBatchSimultaneousCountBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:133
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchFamilyMeasure_rewardConsistent_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:158
BanditRLProof.FiniteHorizonRL.MarkovPolicy.multiBatchEmpiricalModelAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:174
BanditRLProof.FiniteHorizonRL.MarkovPolicy.multiBatchCumulativeExpectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:183
BanditRLProof.FiniteHorizonRL.MarkovPolicy.multiBatchCumulativeSelectedRadiusOccupancy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:192
BanditRLProof.FiniteHorizonRL.MarkovPolicy.allCoordinateConfidenceFamily_of_not_mem definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:209
BanditRLProof.FiniteHorizonRL.MarkovPolicy.confidenceFamily_optimism_and_cumulativeExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:251
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchFamily_allCoordinate_finiteBatchModel_confidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:286
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchFamily_allCoordinate_optimism_and_cumulativeExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret Compiled BanditRLProof/RL/FiniteHorizonIIDMultiBatchCumulativeConfidenceRegret.lean:339
BanditRLProof.FiniteHorizonRL.CountCoordinate inductive type Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:31
BanditRLProof.FiniteHorizonRL.CountCoordinate.equivVisitSumTransition definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:40
BanditRLProof.FiniteHorizonRL.countCoordinateCard definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:63
BanditRLProof.FiniteHorizonRL.countCoordinateCard_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:70
BanditRLProof.FiniteHorizonRL.simultaneousCountDelta definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:80
BanditRLProof.FiniteHorizonRL.simultaneousCountConfidenceRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:85
BanditRLProof.FiniteHorizonRL.CountCoordinate.deviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:94
BanditRLProof.FiniteHorizonRL.CountCoordinate.measurable_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:111
BanditRLProof.FiniteHorizonRL.CountCoordinate.badEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:126
BanditRLProof.FiniteHorizonRL.CountCoordinate.measurableSet_badEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:138
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measure_countCoordinate_badEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:153
BanditRLProof.FiniteHorizonRL.MarkovPolicy.simultaneousCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:176
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurableSet_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:186
BanditRLProof.FiniteHorizonRL.MarkovPolicy.simultaneousCountDelta_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:200
BanditRLProof.FiniteHorizonRL.MarkovPolicy.simultaneousCountDelta_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:212
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_simultaneousCountBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:228
BanditRLProof.FiniteHorizonRL.MarkovPolicy.countCoordinate_abs_deviation_lt_of_not_mem_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:271
BanditRLProof.FiniteHorizonRL.MarkovPolicy.visitCount_abs_deviation_lt_of_not_mem_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:290
BanditRLProof.FiniteHorizonRL.MarkovPolicy.transitionCount_abs_deviation_lt_of_not_mem_simultaneousCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:307
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_simultaneous_count_confidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDSimultaneousCountConfidence Compiled BanditRLProof/RL/FiniteHorizonIIDSimultaneousCountConfidence.lean:328
BanditRLProof.FiniteHorizonRL.MDP.trajectoryStateAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:33
BanditRLProof.FiniteHorizonRL.MDP.episodeStepOfTrajectory definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:42
BanditRLProof.FiniteHorizonRL.MDP.episodeBatchOfTrajectories definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:52
BanditRLProof.FiniteHorizonRL.MDP.trajectoryVisitContribution definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:59
BanditRLProof.FiniteHorizonRL.MDP.trajectoryRewardContribution definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:66
BanditRLProof.FiniteHorizonRL.MDP.trajectoryTransitionContribution definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:73
BanditRLProof.FiniteHorizonRL.MDP.measurable_episodeStepOfTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:84
BanditRLProof.FiniteHorizonRL.MDP.measurable_episodeBatchOfTrajectories theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:92
BanditRLProof.FiniteHorizonRL.MDP.episodeBatchOfTrajectories_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:101
BanditRLProof.FiniteHorizonRL.MDP.episodeBatchOfTrajectories_visitCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:113
BanditRLProof.FiniteHorizonRL.MDP.episodeBatchOfTrajectories_rewardSum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:128
BanditRLProof.FiniteHorizonRL.MDP.episodeBatchOfTrajectories_transitionCount theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:143
BanditRLProof.FiniteHorizonRL.MDP.measurable_trajectoryVisitContribution theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:158
BanditRLProof.FiniteHorizonRL.MDP.measurable_trajectoryRewardContribution theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:165
BanditRLProof.FiniteHorizonRL.MDP.measurable_trajectoryTransitionContribution theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:172
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidTrajectoryFamilyMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:184
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:201
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidTrajectoryFamilyMeasure_map_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:221
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatchMeasure_map_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:239
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_episodeStepOfTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:273
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_iidEpisodeBatch_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:288
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_iidEpisodeBatch_statistic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:342
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_episodeStatistic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:360
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_trajectoryVisitContribution theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:377
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_trajectoryRewardContribution theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:393
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iIndepFun_trajectoryTransitionContribution theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:409
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidEpisodeBatch_stepLaw_and_independence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonIIDTrajectoryBatch Compiled BanditRLProof/RL/FiniteHorizonIIDTrajectoryBatch.lean:430
BanditRLProof.FiniteHorizonRL.MDP structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonMDP Compiled BanditRLProof/RL/FiniteHorizonMDP.lean:25
BanditRLProof.FiniteHorizonRL.MDP.transitionValue definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonMDP Compiled BanditRLProof/RL/FiniteHorizonMDP.lean:46
BanditRLProof.FiniteHorizonRL.MDP.bellmanQ definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonMDP Compiled BanditRLProof/RL/FiniteHorizonMDP.lean:52
BanditRLProof.FiniteHorizonRL.MDP.measurable_transitionValue theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonMDP Compiled BanditRLProof/RL/FiniteHorizonMDP.lean:58
BanditRLProof.FiniteHorizonRL.MDP.measurable_bellmanQ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonMDP Compiled BanditRLProof/RL/FiniteHorizonMDP.lean:65
BanditRLProof.FiniteHorizonRL.MDP.bellmanQ_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonMDP Compiled BanditRLProof/RL/FiniteHorizonMDP.lean:73
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:40
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageReturnDeviationProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:58
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixReturnDelta definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:76
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixReturnDelta_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:79
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixReturnDelta_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:84
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_naturalAllPrefixReturnDelta theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:93
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixAverageReturnConfidenceRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:104
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixAverageReturnConfidenceEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:114
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.log_two_div_naturalAllPrefixReturnDelta_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:123
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixAverageReturnConfidenceEnvelope_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:152
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixAverageReturnConfidenceRadius_le_envelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:161
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixAverageReturnConfidenceEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:257
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixAverageReturnConfidenceRadius_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:320
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.naturalAllPrefixReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:339
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_naturalAllPrefixReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:355
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_naturalAllPrefixReturnBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:371
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_naturalAllPrefixReturnBadEvent_measure_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:397
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_eventually_not_mem_naturalAllPrefixReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:422
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_naturalAverageBehaviorExpectedRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:447
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_naturalAverageReturnDeviation_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:483
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_naturalAverageRealizedBehaviorRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureConsistency.lean:557
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageBehaviorRegretL1SummableEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageReturnL1SummableEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:42
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretL1SummableEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:50
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicAverageIntegratedBehaviorExpectedRegretRate_explicitRounds_le_summableEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:59
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageReturnFirstMomentBound_explicitRounds_le_summableEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:99
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretL1SummableEnvelope_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:131
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretL1Envelope_explicitRounds_le_summableEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:150
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_explicitPolynomialPrefixAverageBehaviorRegretL1SummableEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:169
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_explicitPolynomialPrefixAverageReturnL1SummableEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:188
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_explicitPolynomialPrefixAverageRealizedBehaviorRegretL1SummableEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:211
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixExpectedAbsoluteAverageRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:224
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixExpectedAbsoluteAverageRealizedBehaviorRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:237
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixExpectedAbsoluteAverageRealizedBehaviorRegret_le_summableEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:253
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_explicitPolynomialPrefixExpectedAbsoluteAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:282
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixReciprocalThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:314
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixReciprocalThreshold_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:317
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretDistanceViolationProbability_le_expectedAbsolute_div theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:323
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_explicitPolynomialPrefixAverageRealizedBehaviorRegretDistanceViolationProbability_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:399
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_eventually_not_mem_explicitPolynomialPrefixAverageRealizedBehaviorRegretReciprocalDistanceViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:435
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:470
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_explicitPolynomialPrefixAverageRealizedBehaviorRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretAlmostSureExplicitSchedule.lean:523
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_naturalCumulativeSuccessorAverageReturnDeviation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:33
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeReturnDeviationProcess_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:91
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageReturnFirstMomentBound definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:126
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageReturnInverseSqrtEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:136
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageReturnFirstMomentBound_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:147
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integral_abs_selfConsistentScheduledNaturalCausalCumulativeReturnDeviationProcess_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:156
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageReturnFirstMomentBound_le_inverseSqrtEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:189
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageReturnInverseSqrtEnvelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:235
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageReturnFirstMomentBound_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:251
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalCumulativeReturnDeviationProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:270
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:292
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteAverageRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:340
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretL1Envelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:356
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretL1Envelope_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:368
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretL1Envelope_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:383
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteAverageRealizedBehaviorRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:397
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteAverageRealizedBehaviorRegret_le_L1Envelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:411
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteAverageRealizedBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:537
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:570
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:595
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:625
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:660
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretLp definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:695
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretLp_coeFn_ae_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:717
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretLp_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:746
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_naturalAverageRealizedBehaviorRegret_allPrefix_L1_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalAverageRealizedBehaviorRegretL1Consistency.lean:797
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativePlanningRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:46
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativePlanningRate_le_integrated theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:55
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativePlanningRate_le_logarithmic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:73
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalModelFailureBudget_eq_fin_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:87
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.not_mem_selfConsistentScheduledCausalModelRoundBadEvent_of_not_mem_prefix theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:100
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:138
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretProcess_le_planning_of_not_mem_modelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:156
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretProcess_le_logarithmic_of_not_mem_modelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:197
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretLogarithmicViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:232
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretLogarithmicViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:251
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretLogarithmicViolationSet_subset_modelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:269
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_cumulativeBehaviorExpectedRegretLogarithmicViolationSet_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:299
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_fixedPrefixHighProbabilityLogarithmicCumulativeBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretHighProbabilityLogRate.lean:350
BanditRLProof.sum_range_one_div_natCast_add_two_sq_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:41
BanditRLProof.sum_range_one_div_natCast_add_two_pow_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:68
BanditRLProof.sum_range_one_div_natCast_add_three_le_one_add_log theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:83
BanditRLProof.one_le_one_add_log_natCast theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:106
BanditRLProof.tendsto_one_add_log_natCast_div_natCast_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:114
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSquareRateCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:149
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExplorationHarmonicRateCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:154
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalHighPowerRateCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:158
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicRateCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:162
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRefinedCumulativeIntegratedBehaviorExpectedRegretRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:168
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicCumulativeIntegratedBehaviorExpectedRegretRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:175
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicAverageIntegratedBehaviorExpectedRegretRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:180
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalIntegratedBehaviorExpectedRegretRateAt_eq_threeTerm theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:189
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSquareRateCoefficient_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:212
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExplorationHarmonicRateCoefficient_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:221
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalHighPowerRateCoefficient_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:230
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicRateCoefficient_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:239
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeIntegratedBehaviorExpectedRegretRate_le_refined theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:252
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRefinedCumulativeIntegratedBehaviorExpectedRegretRate_le_logarithmic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:297
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeIntegratedBehaviorExpectedRegretRate_le_logarithmic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:325
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicCumulativeIntegratedBehaviorExpectedRegretRate_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:339
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicAverageIntegratedBehaviorExpectedRegretRate_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:352
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicAverageIntegratedBehaviorExpectedRegretRate_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:365
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicCumulativeIntegratedBehaviorExpectedRegretRate_isBigO theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:382
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedCumulativeBehaviorRegret_le_logarithmic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:392
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedCumulativeBehaviorRegret_isBigO_one_add_log theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:419
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegret_le_logarithmic theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:473
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegret_isBigO_log_div_natCast theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:502
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegret_tendsto_zero_of_logarithmicRate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:567
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_cumulative_and_averageBehaviorExpectedRegret_explicitLogarithmicRate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBehaviorExpectedRegretLogRate.lean:600
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretProcess_le_rounds_mul_two_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret.lean:31
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretSecondMomentEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret.lean:67
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretSecondMomentEnvelope_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret.lean:78
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integral_sq_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_le_secondMomentEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret.lean:88
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingExplicitSecondMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret.lean:246
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingExplicitSecondMomentBudget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret.lean:254
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppedAverageRealizedBehaviorRegretSecondMoment_le_explicitBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret.lean:267
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_boundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitDeterministicMomentExpectedAverageRealizedBehaviorRegret.lean:369
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_two_selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:31
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_two_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:84
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_two_selfConsistentScheduledNaturalCausalStoppedAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:136
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRealizedAverageLogarithmicRate_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:170
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingExplicitExpectedRateBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:186
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingExplicitExpectedRateBudget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:196
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppedRealizedAverageLogarithmicRate_le_explicitExpectedRateBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:208
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppedAverageRealizedBehaviorRegretSecondMoment definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:246
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppedAverageRealizedBehaviorRegretSecondMoment_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:266
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_boundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitExpectedAverageRealizedBehaviorRegret.lean:288
BanditRLProof.sum_range_one_div_natCast_add_two_pow_le_one_div_sixteen theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret.lean:23
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalModelFailureBudget_eq_ofReal_two_mul_sum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret.lean:85
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalModelFailureBudget_le_one_eighth theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret.lean:156
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_boundedStoppingSingleModelReturnBadEvent_le_one_quarter theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret.lean:180
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_boundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeExplicitThreeQuarterGoodEventAverageRealizedBehaviorRegret.lean:260
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.one_le_untopA_and_untopA_le_of_withTop_bounds theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRealizedAverageLogarithmicRate_stronglyAdapted theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:61
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppedAverageRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:83
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppedAverageRealizedBehaviorRegret_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:105
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppedRealizedAverageLogarithmicRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:130
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppedRealizedAverageLogarithmicRate_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:156
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingTimeAverageRealizedBehaviorRegretViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:180
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalBoundedStoppingTimeAverageRealizedBehaviorRegretViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:205
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalPositivePrefixAverageRealizedBehaviorRegretViolationWindow definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:244
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalPositivePrefixAverageRealizedBehaviorRegretViolationWindow theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:262
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingTimeAverageRealizedBehaviorRegretViolationSet_subset_positivePrefixWindow theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:281
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_positivePrefixAverageRealizedBehaviorRegretViolationWindow_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:316
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_boundedStoppingTimeAverageRealizedBehaviorRegretViolationSet_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:390
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_boundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeHighProbabilityAverageRealizedBehaviorRegret.lean:446
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.finiteHorizonBadEvent_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:33
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalModelBadEvent_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:55
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingEqualReturnShare definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:74
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalPositivePrefixIndex_nonempty theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:79
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingEqualReturnShare_spec theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:85
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingReturnBadEventWindow definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:108
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalBoundedStoppingReturnBadEventWindow theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:127
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_boundedStoppingReturnBadEventWindow_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:147
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingSingleModelReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:208
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalPositivePrefixAverageRealizedBehaviorRegretViolationWindow_subset_boundedStoppingSingleModelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:227
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_boundedStoppingSingleModelReturnBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:278
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedStoppingTimeAverageRealizedBehaviorRegretViolationSet_subset_singleModelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:344
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_boundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedStoppingTimeSingleModelEventHighProbabilityAverageRealizedBehaviorRegret.lean:392
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exists_window_offset_untopA_eq_of_withTop_bounds theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:31
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedWindowStoppingL1Budget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:59
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedWindowStoppingL1Budget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:70
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBoundedWindowStoppingL1Budget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:83
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteBoundedWindowStoppingAverageRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:105
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalBoundedWindowStoppingAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:128
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteBoundedWindowStoppingAverageRealizedBehaviorRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:166
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteBoundedWindowStoppingAverageRealizedBehaviorRegret_le_budget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:188
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteBoundedWindowStoppingAverageRealizedBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:306
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalBoundedWindowStoppingAverageRealizedBehaviorRegret_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:357
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalBoundedWindowStoppingAverageRealizedBehaviorRegret_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:402
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_boundedWindowStoppingTimeNaturalAverageRealizedBehaviorRegret_L1_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalBoundedWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:489
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassagePrefixNat definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:39
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:61
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassagePrefixNat_eq_of_first_hit theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:80
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassagePrefixNat_eq_base_of_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:136
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassagePrefixNat_eq_right_of_forall_lt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:164
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassagePrefixNat_before_gt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:210
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassagePrefixNat_le_threshold_of_lt_right theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:233
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingPrefix_isStoppingTime theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:259
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingPrefix_lower theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:293
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingPrefix_upper theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:320
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_cappedDoubleLinearRawWindowFirstPassageStoppingTimeNaturalAverageRealizedBehaviorRegret_L1_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalCappedDoubleLinearRawWindowFirstPassageStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:351
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityRounds_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.scheduleIndex_le_explicitHighProbabilityRounds_add theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:42
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exists_growingWindowGrid_offset_untopA_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:50
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.growingWindowGrid_stoppingPrefix_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:73
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalGrowingWindowGridStoppingL1Budget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:90
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalGrowingWindowGridStoppingL1Tail definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:99
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalGrowingWindowGridStoppingL1Budget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:111
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalGrowingWindowGridStoppingL1Budget_le_tail theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:124
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalGrowingWindowGridStoppingL1Tail_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:151
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalGrowingWindowGridStoppingL1Budget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:165
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteGrowingWindowGridStoppingAverageRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:183
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalGrowingWindowGridStoppingAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:206
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteGrowingWindowGridStoppingAverageRealizedBehaviorRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:248
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteGrowingWindowGridStoppingAverageRealizedBehaviorRegret_le_budget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:270
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteGrowingWindowGridStoppingAverageRealizedBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:410
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalGrowingWindowGridStoppingAverageRealizedBehaviorRegret_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:458
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalGrowingWindowGridStoppingAverageRealizedBehaviorRegret_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:505
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_growingWindowGridStoppingTimeNaturalAverageRealizedBehaviorRegret_L1_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalGrowingWindowGridStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:588
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtFirstPassageThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:30
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtFirstPassageThreshold_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtFirstPassageThreshold_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:47
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageStoppingPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:58
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayedSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:77
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayedProbability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:96
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:113
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayedSet_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:123
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayedSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:215
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayedSet_subset_distanceViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:236
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.sqrt_div_pow_three_eq_inverse_rpow_five_halves lemma Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:271
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.sqrt_div_pow_two_eq_inverse_rpow_three_halves lemma Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:279
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayRate_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:292
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixExpectedAbsoluteAverageRealizedBehaviorRegret_div_inverseSqrtFirstPassageThreshold_le_delayRate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:341
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayRate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:378
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayRate_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:437
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayedProbability_le_rate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:447
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayedProbability_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:519
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_eventually_not_mem_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayedSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:550
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_eventually_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageStoppingPrefix_eq_base theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:585
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageDelayedProbability_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:633
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassage_summableDelay_eventuallyImmediateStopping_and_L1_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageSummableDelayAndEventualImmediateStoppingL1Consistency.lean:667
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integral_tendsto_zero_of_memLp_one_of_eLpNorm_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement.lean:31
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretIntegralDifference_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement.lean:55
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretExpectedGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement.lean:136
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretExpectedGapAbs_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement.lean:233
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageRealizedBehaviorRegretIntegral_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement.lean:280
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_expected_truncation_replacement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterExpectedRegretTruncationReplacement.lean:343
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppingPrefixes_eq_base_of_not_mem_delayedSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_eventually_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageRealizedBehaviorRegret_eq_unboundedHittingAfter theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:120
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:172
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageRealizedBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:213
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretDifference theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:274
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretDifference_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:322
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretDifferenceLp definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:439
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretDifferenceLp_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:481
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretDifference_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:564
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_L1_truncation_equivalence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterL1TruncationEquivalence.lean:627
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorBatchAverageSampledReturn definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:35
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalAverageSampledReturn definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:47
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalAverageSampledReturn_eq_optimal_sub_naturalAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:67
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalAverageSampledReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:97
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalAverageSampledReturn_naturalTrajectoryFiltration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:121
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalAverageSampledReturn_stronglyAdapted_naturalTrajectoryFiltration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:148
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageSampledReturnProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:167
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageSampledReturnProcess_eq_optimal_sub_realized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:184
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageSampledReturnProcess_stronglyAdapted theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:209
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledReturnProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:229
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledReturnProcess_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:253
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledReturnProcess_eq_optimal_sub_realized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:275
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledReturnProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:304
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledReturnProcess_of_integrable_realized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:341
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integral_selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledReturnProcess_eq_optimal_sub_realized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:355
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSampledReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:370
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSampledReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:431
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSampledReturnIntegral_eq_optimal_sub_realized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:492
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSampledReturnIntegral_eq_optimal_sub_realized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:548
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSampledReturnIntegral_tendsto_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:604
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSampledReturnIntegral_tendsto_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:671
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedAverageSampledReturn_expected_optimality theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedAverageSampledReturnExpectedOptimality.lean:738
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretExpectedGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement.lean:32
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretExpectedGapAbs_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement.lean:126
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnDeviationExpectedGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement.lean:174
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnDeviationExpectedGapAbs_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement.lean:270
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageRealizedBehaviorRegretIntegral_eq_behaviorExpected_sub_returnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement.lean:317
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretIntegral_eq_behaviorExpected_sub_returnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement.lean:399
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedBehaviorExpectedRegret_and_returnDeviation_expected_truncation_replacement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationExpectedTruncationReplacement.lean:481
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_tendsto_untopA_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedDoubleLinearRawWindowFirstPassageStoppingPrefix_atTop theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:34
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_eventually_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegret_and_returnDeviation_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:72
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCapped_stoppedBehaviorExpectedRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:140
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:185
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:215
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedBehaviorExpectedRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:256
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedBehaviorExpectedRegretIntegral_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:373
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:414
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedReturnDeviation_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:490
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedReturnDeviationIntegral_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:606
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretDifference theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:649
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretDifference_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:690
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretDifferenceIntegral_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:800
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnDeviationDifference_eq_behaviorExpectedRegretDifference_sub_realizedBehaviorRegretDifference theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:850
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnDeviationDifference theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:921
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnDeviationDifference_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:970
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnDeviationDifferenceIntegral_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:1118
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedBehaviorExpectedRegret_and_returnDeviation_L1_truncation_equivalence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1TruncationEquivalence.lean:1169
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageRealizedBehaviorRegretIntegral_sub_behaviorExpectedRegretIntegral_eq_neg_returnDeviationIntegral theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency.lean:32
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretIntegral_sub_behaviorExpectedRegretIntegral_eq_neg_returnDeviationIntegral theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency.lean:79
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageRealizedBehaviorRegretPolicyValueExpectedGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency.lean:124
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageRealizedBehaviorRegretPolicyValueExpectedGapAbs_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency.lean:203
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretPolicyValueExpectedGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency.lean:247
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretPolicyValueExpectedGapAbs_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency.lean:326
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedRealizedBehaviorRegret_and_policyValue_expected_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedRealizedBehaviorRegretAndPolicyValueExpectedConsistency.lean:372
BanditRLProof.FiniteHorizonRL.probReal_compl_gt_one_sub_of_measure_lt_ofReal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality.lean:25
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointGoodSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality.lean:54
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointGoodSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality.lean:72
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.mem_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointGoodSet_iff theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality.lean:91
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointGoodSet_probReal_gt_one_sub theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality.lean:157
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exists_tailStart_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointViolationProbability_lt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality.lean:202
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedSampledReturn_and_successorPolicyExpectedReturn_deterministicTailHighProbability_optimality theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnDeterministicTailHighProbabilityOptimality.lean:231
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCapped_stoppedAverageRealizedBehaviorRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageReturnDeviationProcess_eq_behaviorExpected_sub_realized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:82
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSampledReturn_tendstoInMeasure_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:115
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSampledReturn_tendstoInMeasure_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:161
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSuccessorPolicyExpectedReturn_tendstoInMeasure_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:207
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSuccessorPolicyExpectedReturn_tendstoInMeasure_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:252
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedSampledPolicyExpectedReturnGap_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:297
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedSampledPolicyExpectedReturnGap_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:344
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCapped_stoppedAverageSampledReturn_tendstoAlmostEverywhere_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:391
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageSampledReturn_tendstoAlmostEverywhere_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:454
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCapped_stoppedAverageSuccessorPolicyExpectedReturn_tendstoAlmostEverywhere_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:517
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageSuccessorPolicyExpectedReturn_tendstoAlmostEverywhere_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:580
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCapped_stoppedSampledPolicyExpectedReturnGap_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:643
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedSampledPolicyExpectedReturnGap_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:720
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedSampledReturn_and_successorPolicyExpectedReturn_inMeasure_and_almostSure_optimality theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnInMeasureAlmostSureOptimality.lean:798
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_fun_neg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:39
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledReturnOptimalityErrorProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:46
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSuccessorPolicyExpectedReturnOptimalityErrorProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:73
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledPolicyExpectedReturnGapProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:99
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledReturnOptimalityErrorProcess_eq_neg_realized theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:127
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSuccessorPolicyExpectedReturnOptimalityErrorProcess_eq_neg_behaviorExpected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:155
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledPolicyExpectedReturnGapProcess_eq_returnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:183
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedSampledReturnOptimalityError theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:210
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedSampledReturnOptimalityError_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:246
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedSampledReturnOptimalityError theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:286
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedSampledReturnOptimalityError_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:323
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedSuccessorPolicyExpectedReturnOptimalityError theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:363
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedSuccessorPolicyExpectedReturnOptimalityError_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:393
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedSuccessorPolicyExpectedReturnOptimalityError theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:433
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedSuccessorPolicyExpectedReturnOptimalityError_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:463
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedSampledPolicyExpectedReturnGap theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:502
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedSampledPolicyExpectedReturnGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:538
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedSampledPolicyExpectedReturnGap theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:576
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedSampledPolicyExpectedReturnGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:613
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedSampledReturn_and_successorPolicyExpectedReturn_L1_optimality theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnL1Optimality.lean:653
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSampledReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:32
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSampledReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:61
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedSampledPolicyExpectedReturnGap theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:86
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedSampledPolicyExpectedReturnGap theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:112
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:139
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:198
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.not_mem_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointViolationSet_iff theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:250
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointViolationProbability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:313
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointViolationProbability_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:328
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eventually_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointViolationProbability_lt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:481
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedSampledReturn_and_successorPolicyExpectedReturn_simultaneousHighProbability_optimality theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledAndSuccessorPolicyReturnSimultaneousHighProbabilityOptimality.lean:512
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorPolicyExpectedReturn definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:39
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorPolicyExpectedReturn_eq_optimal_sub_expectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:55
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalAverageSuccessorPolicyExpectedReturn definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:72
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalAverageSuccessorPolicyExpectedReturn_eq_optimal_sub_expectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:92
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageSuccessorPolicyExpectedReturnProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:131
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageSuccessorPolicyExpectedReturnProcess_eq_optimal_sub_behaviorExpected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:150
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalAverageSuccessorPolicyExpectedReturnProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:179
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSuccessorPolicyExpectedReturnProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:213
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSuccessorPolicyExpectedReturnProcess_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:238
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSuccessorPolicyExpectedReturnProcess_eq_optimal_sub_behaviorExpected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:263
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalStoppingTimeAverageSuccessorPolicyExpectedReturnProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:295
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_stoppedSuccessorPolicyExpectedReturn_of_integrable_behavior theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:340
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integral_stoppedSuccessorPolicyExpectedReturn_eq_optimal_sub_behavior theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:354
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageSampledReturn_sub_successorPolicyExpectedReturn_eq_returnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:369
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSuccessorPolicyExpectedReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:400
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSuccessorPolicyExpectedReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:430
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSuccessorPolicyExpectedReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:456
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSuccessorPolicyExpectedReturn theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:511
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSuccessorPolicyExpectedReturnIntegral_eq_optimal_sub_behaviorExpected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:566
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSuccessorPolicyExpectedReturnIntegral_eq_optimal_sub_behaviorExpected theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:616
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSampledReturnIntegral_sub_successorPolicyExpectedReturnIntegral_eq_returnDeviationIntegral theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:666
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSampledReturnIntegral_sub_successorPolicyExpectedReturnIntegral_eq_returnDeviationIntegral theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:725
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSampledReturnSuccessorPolicyExpectedReturnGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:783
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSampledReturnSuccessorPolicyExpectedReturnGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:859
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSampledReturnSuccessorPolicyExpectedReturnAbsGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:935
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSampledReturnSuccessorPolicyExpectedReturnAbsGap_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:976
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedStoppedAverageSuccessorPolicyExpectedReturnIntegral_tendsto_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:1017
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageSuccessorPolicyExpectedReturnIntegral_tendsto_optimal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:1084
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedSampledReturn_and_successorPolicyExpectedReturn_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedSampledReturnAndSuccessorPolicyExpectedReturnConsistency.lean:1151
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:34
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingPrefix_lower theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:56
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingPrefix_eq_base_of_process_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:78
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_untopA_unboundedHittingAfter_le_threshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:109
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingPrefix_isStoppingTime theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:166
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_ne_top_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingPrefix theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:189
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_all_ne_top_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingPrefix theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:260
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_eventually_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingPrefix_eq_base theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:293
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.ae_tendsto_untopA_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingPrefix_atTop theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:333
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedProcess_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:371
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedProcess_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:427
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_aeFinite_eventuallyImmediateStopping_and_inMeasure_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterAEFiniteEventualImmediateStoppingAndInMeasureConsistency.lean:465
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterDegreeFourScale definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:34
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterDegreeFourScale_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:42
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.sqrt_inverseSqrtThresholdUnboundedHittingAfterDegreeEightScale theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:54
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.sqrt_inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentBudget_isBigO_degreeFour theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:73
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzPolynomialAbsoluteFirstMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:92
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzPolynomialAbsoluteFirstMomentBudget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:108
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzPolynomialAbsoluteFirstMomentBudget_isBigO_degreeFour theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:122
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_integrable_and_integral_abs_le_cauchySchwarzPolynomialBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:145
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegretExpectedAbsolute_le_cauchySchwarzPolynomialBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:248
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegretExpectedAbsolute_isBigO_degreeFour theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterCauchySchwarzExpectedAbsoluteAsymptotics.lean:278
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tendsto_integral_abs_restrict_of_uniformIntegrable_one_of_measure_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedEventExpectedContribution Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedEventExpectedContribution.lean:31
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tendsto_abs_integral_restrict_of_uniformIntegrable_one_of_measure_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedEventExpectedContribution Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedEventExpectedContribution.lean:64
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_delayedEvent_expectedContribution_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedEventExpectedContribution Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedEventExpectedContribution.lean:85
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretExpectedPositivePart definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExpectedPositivePartConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExpectedPositivePartConsistency.lean:30
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretExpectedPositivePart_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExpectedPositivePartConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExpectedPositivePartConsistency.lean:52
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegretPositivePart_integrable_and_integral_le_threshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExpectedPositivePartConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExpectedPositivePartConsistency.lean:73
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegretExpectedPositivePart_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExpectedPositivePartConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExpectedPositivePartConsistency.lean:174
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretRateLinearCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:32
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretRateLinearCoefficient_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:45
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretRate_le_linearEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:66
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterExplicitTailStart definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:174
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterExplicitTailStart_spec theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:188
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterTailStart_le_explicitTailStart theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:245
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterExplicitStoppingRoundSecondMomentENNRealBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:262
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterExplicitStoppingRoundSecondMomentENNRealBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:278
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterExplicitStoppingRoundSecondMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:293
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitStoppingRoundSecondMomentENNRealBudgetAt_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:305
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterStoppingRoundSecondMomentENNRealBudget_le_explicit theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:322
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterStoppingRoundSecondMomentBudget_le_explicit theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:339
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_integral_stoppingRound_sq_le_explicitTailStartBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:359
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartDeterministicStoppingRoundSecondMomentAbsoluteFirstMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:397
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_integrable_and_integral_abs_le_explicitTailStartDeterministicStoppingRoundSecondMomentBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterExplicitTailStartExpectedAbsoluteBound.lean:413
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretUniformSecondMomentEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:34
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretUniformSecondMomentEnvelope_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:43
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingFiberAbsoluteFirstMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:55
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingRoundSecondMomentAbsoluteFirstMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:82
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDeterministicStoppingRoundSecondMomentAbsoluteFirstMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:110
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integral_sq_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_le_uniformSecondMomentEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:125
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_integrable_and_integral_le_threshold theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:217
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_integrable_and_integral_abs_le_stoppingFiberBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:330
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_integrable_and_integral_abs_le_stoppingRoundSecondMomentBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:426
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_integrable_and_integral_abs_le_deterministicStoppingRoundSecondMomentBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableExpectedUpperBound.lean:522
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityQuarticBlockWeight definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:42
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityRounds_succ_sub_le_quarticBlockWeight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:49
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledLocalDelta_le_inv_pow_six theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:64
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.quarticBlockShiftedInverseCubePairEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:75
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticBlockShiftedInverseCubePairEnvelope_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:84
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.quarticBlockShiftedCoordinateModelFailureCharge definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:179
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.quarticBlockShiftedCoordinateModelFailureCharge_le_pairEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:189
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticBlockShiftedCoordinateModelFailureCharge_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:259
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.quarticBlockWeight_mul_tailModelFailureBudget_eq_tsum_shiftedCoordinateCharge theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:273
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticBlockWeight_mul_tailModelFailureBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:299
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_quarticBlockWeight_mul_explicitHighProbabilityReturnDelta theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:321
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticBlockWeight_mul_explicitHighProbabilityReturnDelta_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:358
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticBlockWeight_mul_explicitPolynomialPrefixTailModelReturnFailureBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:377
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityRounds_add_le_add_sum_Ico_quarticBlockWeight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:397
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.natCast_succ_le_checkpoint_add_tsum_quarticBlockWeight_of_delayed theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:440
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_untopA_add_one_of_eventually_quarticCheckpointTail theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:539
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedCheckpointSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:646
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedCheckpointSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:665
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedCheckpointSet_subset_explicitPolynomialPrefixAverageRealizedBehaviorRegretViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:687
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eventually_selfConsistentScheduledCausalSource_trajectoryMeasure_inverseSqrtThresholdUnboundedHittingAfterDelayedCheckpointSet_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:741
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_integrableFiniteStoppingTime theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterIntegrableFiniteStoppingTime.lean:791
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalAverageRealizedBehaviorRegret_succ_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:37
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_naturalSuccessorAverageReturnDeviationIncrement_succ_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:63
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorAverageReturnVarianceProxyAt_succ_le_globalReturnDeviationPerEpisodeVarianceProxy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:115
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorBatchAverageRealizedRegretSecondMomentEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:149
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.memLp_two_naturalSuccessorBatchAverageRealizedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:157
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.integral_sq_naturalSuccessorBatchAverageRealizedRegret_le_secondMomentEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:214
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.max_neg_natWeightedAverage_succ_le_abs_increment_div theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:334
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.hittingAfter_predecessor_gt_of_untopA_gt_base theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:353
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterDelayedReciprocalWeight definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:383
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.max_neg_hittingAfter_untopA_le_base_abs_add_abs_stoppedValue_delayedReciprocalIncrement theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:390
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_inverseSqrtThresholdUnboundedHittingAfterDelayedReciprocalWeight_sq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:487
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterDelayedReciprocalWeight_sq_tsum_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:508
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterDelayedReciprocalWeight_sq_tsum_sqrt_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:537
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedReciprocalSuccessorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:549
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfter_stoppedNegativePart_le_baseAbsolute_add_delayedReciprocalSuccessorRegretAbsolute theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:577
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_delayedReciprocalSuccessorRegret_integrable_and_integral_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:648
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterDelayedReciprocalSuccessorRegretExpectedAbsolute definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:757
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_delayedReciprocalSuccessorRegretExpectedAbsolute_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:774
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretExpectedNegativePart definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:827
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegretExpectedNegativePart_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:851
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegretExpectedAbsolute_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterL1Consistency.lean:1004
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency.lean:30
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegret_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency.lean:67
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency.lean:110
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegret_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency.lean:154
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretLp definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency.lean:197
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretLp_coeFn_ae_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency.lean:231
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretLp_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency.lean:272
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_memLp_eLpNorm_Lp_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterLpConsistency.lean:330
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterDegreeEightScale definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:32
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterDegreeEightScale_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:40
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterDegreeEightScale_one_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:50
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialCheckpointAsymptoticCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:60
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialCheckpointSquare_le_asymptoticCoefficient_mul_scale_pow_eight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:71
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentAsymptoticCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:108
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentAsymptoticCoefficient_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:119
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentBudget_le_asymptoticCoefficient_mul_degreeEightScale theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:134
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentBudget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:219
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentBudget_isBigO_degreeEight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:234
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingRoundSecondMoment definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:260
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppingRoundSecondMoment_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:277
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppingRoundSecondMoment_le_polynomialBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:295
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_integral_stoppingRound_sq_isBigO_degreeEight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:323
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterShiftedInverseSquareSeriesConstant definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:363
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterShiftedInverseSquareSeriesConstant_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:371
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialAbsoluteFirstMomentAsymptoticCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:379
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialAbsoluteFirstMomentAsymptoticCoefficient_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:393
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentAbsoluteFirstMomentBudget_le_asymptoticCoefficient_mul_degreeEightScale theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:411
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentAbsoluteFirstMomentBudget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:515
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentAbsoluteFirstMomentBudget_isBigO_degreeEight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:542
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretExpectedAbsolute definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:568
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretExpectedAbsolute_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:589
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegretExpectedAbsolute_le_polynomialBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:607
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegretExpectedAbsolute_isBigO_degreeEight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteAsymptotics.lean:637
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialScaleCoefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:32
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterExplicitTailStart_succ_le_polynomialScale theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:44
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialCheckpointSquare definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:104
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterExplicitCheckpointSquare_le_polynomial theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:117
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterWeightedFailureSecondMomentENNRealConstant definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:138
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterWeightedFailureSecondMomentENNRealConstant_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:149
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterWeightedFailureSecondMomentConstant definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:160
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentENNRealBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:167
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentENNRealBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:180
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:195
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentENNRealBudget_toReal theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:209
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterExplicitStoppingRoundSecondMomentENNRealBudget_le_polynomial theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:230
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterExplicitStoppingRoundSecondMomentBudget_le_polynomial theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:253
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_integral_stoppingRound_sq_le_polynomialBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:281
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialStoppingRoundSecondMomentAbsoluteFirstMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:318
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_integrable_and_integral_abs_le_polynomialStoppingRoundSecondMomentBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterPolynomialSecondMomentExpectedAbsoluteBound.lean:333
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityQuarticSquareBlockWeight definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityRounds_succ_square_sub_le_quarticSquareBlockWeight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:43
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledLocalDelta_le_inv_pow_ten theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:58
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.quarticSquareBlockShiftedInverseCubePairEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:69
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticSquareBlockShiftedInverseCubePairEnvelope_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:77
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.quarticSquareBlockShiftedCoordinateModelFailureCharge definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:88
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.quarticSquareBlockShiftedCoordinateModelFailureCharge_le_pairEnvelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:98
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticSquareBlockShiftedCoordinateModelFailureCharge_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:170
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.quarticSquareBlockWeight_mul_tailModelFailureBudget_eq_tsum_shiftedCoordinateCharge theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:184
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticSquareBlockWeight_mul_tailModelFailureBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:210
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.summable_quarticSquareBlockWeight_mul_explicitHighProbabilityReturnDelta theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:232
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticSquareBlockWeight_mul_explicitHighProbabilityReturnDelta_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:269
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.tsum_quarticSquareBlockWeight_mul_explicitPolynomialPrefixTailModelReturnFailureBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:288
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityRounds_add_square_le_add_sum_Ico_quarticSquareBlockWeight theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:309
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.natCast_succ_square_le_checkpoint_square_add_tsum_quarticSquareBlockWeight_of_delayed theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:358
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exists_inverseSqrtThresholdUnboundedHittingAfterTailStart theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:468
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterTailStart definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:490
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterTailStart_spec theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:500
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterStoppingRoundSecondMomentENNRealBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:520
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterStoppingRoundSecondMomentENNRealBudget_ne_top theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:533
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.inverseSqrtThresholdUnboundedHittingAfterStoppingRoundSecondMomentBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:549
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.lintegral_sq_untopA_add_one_le_quarticSquareCheckpointBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:561
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_two_untopA_add_one_of_eventually_quarticSquareCheckpointTail theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:660
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_inverseSqrtThresholdUnboundedHittingAfterDelayedCheckpointSet_le_of_tailStart theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:773
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_lintegral_stoppingRound_sq_le_ENNRealBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:826
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_squareIntegrableFiniteStoppingTime theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:876
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_integral_stoppingRound_sq_le_budget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterSquareIntegrableFiniteStoppingTime.lean:928
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageBehaviorExpectedRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageBehaviorExpectedRegretProcess_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:60
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageReturnDeviationProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:88
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageReturnDeviationProcess_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:113
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:142
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegretProcess_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:161
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageBehaviorExpectedRegretProcess_le_two_mul_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:185
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalStoppingTimeAverageBehaviorExpectedRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:217
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageBehaviorExpectedRegretProcess_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:255
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageBehaviorExpectedRegretProcess_le_two_mul_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:283
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageRealizedBehaviorRegretProcess_eq_behaviorExpected_sub_returnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:313
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedBehaviorExpectedRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:350
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:396
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integrable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:422
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:468
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integral_abs_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:496
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegret_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:591
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:624
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretIntegral_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:667
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:708
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedReturnDeviation_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:784
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedReturnDeviationIntegral_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:896
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedBehaviorExpectedRegret_and_returnDeviation_L1_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedBehaviorExpectedRegretAndReturnDeviationL1Consistency.lean:939
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.integral_abs_restrict_le_of_uniformIntegrable_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformAbsoluteContinuity Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformAbsoluteContinuity.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_uniformAbsoluteContinuity theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformAbsoluteContinuity Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformAbsoluteContinuity.lean:68
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.uniformIntegrable_one_of_memLp_and_tendsto_eLpNorm_sub_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformIntegrabilityExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformIntegrabilityExpectedConsistency.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.uniformIntegrable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformIntegrabilityExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformIntegrabilityExpectedConsistency.lean:73
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdUnboundedHittingAfterStoppedAverageRealizedBehaviorRegretIntegral_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformIntegrabilityExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformIntegrabilityExpectedConsistency.lean:128
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdUnboundedHittingAfter_stoppedAverageRealizedBehaviorRegret_uniformIntegrable_and_integral_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformIntegrabilityExpectedConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalInverseSqrtThresholdUnboundedHittingAfterUniformIntegrabilityExpectedConsistency.lean:193
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.one_add_log_le_two_mul_sqrt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:38
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalLogarithmicAverageIntegratedBehaviorExpectedRegretRate_le_inverseSqrt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:49
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRawWindowL1Coefficient definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:79
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRawWindowInverseSqrtL1Envelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:87
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRawWindowL1Coefficient_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:97
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretL1Envelope_le_rawWindowInverseSqrtL1Envelope theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:111
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityScale_sq_le_sqrt_rounds_add theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:149
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRawWindowInverseSqrtL1Envelope_add_le_inverseSquare theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:170
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalPolynomialBaseGrowingRawWindowStoppingL1Budget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:188
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalPolynomialBaseGrowingRawWindowStoppingL1Budget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:201
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalPolynomialBaseGrowingRawWindowStoppingL1Budget_le_rate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:217
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRawWindowL1Rate_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:256
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalPolynomialBaseGrowingRawWindowStoppingL1Budget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:271
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exists_polynomialBaseGrowingRawWindow_offset_untopA_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:289
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsolutePolynomialBaseGrowingRawWindowStoppingAverageRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:308
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalPolynomialBaseGrowingRawWindowStoppingAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:331
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsolutePolynomialBaseGrowingRawWindowStoppingAverageRealizedBehaviorRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:371
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsolutePolynomialBaseGrowingRawWindowStoppingAverageRealizedBehaviorRegret_le_budget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:393
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsolutePolynomialBaseGrowingRawWindowStoppingAverageRealizedBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:526
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalPolynomialBaseGrowingRawWindowStoppingAverageRealizedBehaviorRegret_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:577
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalPolynomialBaseGrowingRawWindowStoppingAverageRealizedBehaviorRegret_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:623
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_explicitPolynomialBaseGrowingRawWindowStoppingTimeNaturalAverageRealizedBehaviorRegret_L1_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalPolynomialBaseGrowingRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:708
BanditRLProof.measurable_apply_randomNat theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency.lean:27
BanditRLProof.ae_tendsto_apply_randomPrefix theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency.lean:41
BanditRLProof.tendsto_randomPrefix_atTop_of_nat_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency.lean:56
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRandomPrefixAverageRealizedBehaviorRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency.lean:78
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRandomPrefixAverageRealizedBehaviorRegretProcess_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency.lean:101
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalRandomPrefixAverageRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency.lean:127
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_randomPrefixNaturalAverageRealizedBehaviorRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency.lean:161
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_randomPrefixNaturalAverageRealizedBehaviorRegret_tendstoAlmostEverywhere_zero_of_nat_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRandomPrefixAverageRealizedBehaviorRegretAlmostSureConsistency.lean:221
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRateControlledRawWindowStoppingL1Budget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRateControlledRawWindowStoppingL1Rate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:46
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.sqrt_baseRounds_le_sqrt_add theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:58
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRawWindowInverseSqrtL1Envelope_add_le_base theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:67
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRateControlledRawWindowStoppingL1Budget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:87
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRateControlledRawWindowStoppingL1Budget_le_rate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:103
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRateControlledRawWindowStoppingL1Rate_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:143
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRateControlledRawWindowStoppingL1Budget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:162
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.exists_rateControlledRawWindow_offset_untopA_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:189
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityRawWindowCandidateRate_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:211
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityDoubleLinearRawWindowCandidateRate_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:247
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteRateControlledRawWindowStoppingAverageRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:282
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.memLp_one_selfConsistentScheduledNaturalCausalRateControlledRawWindowStoppingAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:305
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteRateControlledRawWindowStoppingAverageRealizedBehaviorRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:345
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteRateControlledRawWindowStoppingAverageRealizedBehaviorRegret_le_budget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:367
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalExpectedAbsoluteRateControlledRawWindowStoppingAverageRealizedBehaviorRegret_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:493
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalRateControlledRawWindowStoppingAverageRealizedBehaviorRegret_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:551
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eLpNorm_one_selfConsistentScheduledNaturalCausalRateControlledRawWindowStoppingAverageRealizedBehaviorRegret_sub_zero_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:597
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_rateControlledRawWindowStoppingTimeNaturalAverageRealizedBehaviorRegret_L1_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRateControlledRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:689
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBurninCumulativeBehaviorExpectedRegretLogarithmicRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:38
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeBehaviorExpectedRegretProcess_le_burnin_logarithmic_of_not_mem_tailModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:50
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBurninTailModelReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:183
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBurninTailModelReturnFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:201
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_naturalBurninTailModelReturnBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:208
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBurninRealizedCumulativeLogarithmicRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:281
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBurninRealizedAverageLogarithmicRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:293
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeRealizedBehaviorRegretProcess_le_burnin_logarithmic_of_not_mem_tailModelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:306
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_le_burnin_logarithmic_of_not_mem_tailModelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:405
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBurninCumulativeRealizedBehaviorRegretLogarithmicViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:450
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBurninAverageRealizedBehaviorRegretLogarithmicViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:470
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalBurninCumulativeRealizedBehaviorRegretLogarithmicViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:490
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalBurninAverageRealizedBehaviorRegretLogarithmicViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:510
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBurninCumulativeRealizedBehaviorRegretLogarithmicViolationSet_subset_tailModelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:530
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalBurninAverageRealizedBehaviorRegretLogarithmicViolationSet_subset_tailModelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:564
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_burninTailHighProbabilityLogarithmicCumulativeAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityBurninLogRate.lean:601
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalCumulativeSuccessorAverageReturnVarianceProxy_le_rounds_mul theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:40
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityScale definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:92
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityBurnin definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:95
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityRounds definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:99
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityReturnDelta definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:103
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityScale_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:106
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityBurnin_le_rounds theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:110
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityRounds_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:115
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityReturnDelta_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:120
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityReturnDelta_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:124
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityScale_tendsto_atTop theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:129
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityScale_real_tendsto_atTop theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:134
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityRounds_tendsto_atTop theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:139
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitHighProbabilityReturnDelta_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:144
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeReturnVarianceProxy_le_rounds_mul theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:155
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageReturnRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:174
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageReturnRadius_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:187
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageReturnRadius_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:311
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixTailModelReturnFailureBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:329
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:336
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixTailModelReturnFailureBudget_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:349
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretRate_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:374
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixTailModelReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:439
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:457
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_explicitPolynomialPrefixHighProbabilityAverageRealizedBehaviorRegretConsistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityExplicitSchedule.lean:479
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorAverageReturnDeviationIncrement definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:54
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorAverageReturnVarianceProxyAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:68
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalCumulativeSuccessorAverageReturnVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:79
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalCumulativeSuccessorAverageReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:87
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorAverageReturnDeviationIncrement_stronglyAdapted_piLE theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:101
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalCumulativeSuccessorAverageReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:129
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorAverageReturnDeviationIncrement_succ_hasCondSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:146
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalCumulativeSuccessorAverageReturnVarianceProxy_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:185
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.trajectoryMeasure_naturalCumulativeSuccessorAverageReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:227
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalCumulativeSuccessorAverageReturnDeviation_eq_sum_range theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:295
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorBatchAverageRealizedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:311
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalCumulativeRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:324
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalAverageRealizedBehaviorRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:335
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalSuccessorBatchAverageRealizedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:349
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalCumulativeRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:365
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:380
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalSuccessorBatchAverageRealizedRegret_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:395
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalCumulativeRealizedBehaviorRegret_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:421
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeReturnVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:459
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeReturnDeviationProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:470
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeRealizedBehaviorRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:486
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:503
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:519
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalCumulativeReturnDeviationProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:539
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalCumulativeRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:560
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:577
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalCumulativeReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:594
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeRealizedBehaviorRegretProcess_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:612
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_eq_expected_sub_deviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:650
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_naturalCumulativeReturnBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:679
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRealizedCumulativeLogarithmicRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:728
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalRealizedAverageLogarithmicRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:738
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalModelReturnBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:745
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeRealizedBehaviorRegretLogarithmicViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:763
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretLogarithmicViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:782
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalCumulativeRealizedBehaviorRegretLogarithmicViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:801
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretLogarithmicViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:819
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_naturalModelReturnBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:837
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeRealizedBehaviorRegretProcess_le_logarithmic_of_not_mem_modelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:900
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_le_logarithmic_of_not_mem_modelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:991
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalCumulativeRealizedBehaviorRegretLogarithmicViolationSet_subset_modelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:1032
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretLogarithmicViolationSet_subset_modelReturnBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:1063
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_fixedPrefixHighProbabilityLogarithmicCumulativeAverageRealizedBehaviorRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretHighProbabilityLogRate.lean:1100
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:36
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretDistanceViolationSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:52
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretDistanceViolationProbability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:71
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_explicitPolynomialPrefixAverageRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:87
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_explicitPolynomialPrefixAverageRealizedBehaviorRegretDistanceViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:104
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretProcess_neg_averageReturnRadius_lt_of_not_mem_event theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:130
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_explicitPolynomialPrefixTailModelReturnBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:207
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eventually_explicitPolynomialPrefixAverageRealizedBehaviorRegretDistanceViolationSet_subset_event theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:239
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eventually_explicitPolynomialPrefixAverageRealizedBehaviorRegretDistanceViolationProbability_le_failureBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:306
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretDistanceViolationProbability_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:342
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_explicitPolynomialPrefixAverageRealizedBehaviorRegret_tendstoInMeasure_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretInMeasureExplicitSchedule.lean:375
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretUpperTailSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability.lean:34
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretUpperTailProbability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability.lean:53
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_explicitPolynomialPrefixAverageRealizedBehaviorRegretUpperTailSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability.lean:69
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eventually_explicitPolynomialPrefixAverageRealizedBehaviorRegretUpperTailSet_subset_violationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability.lean:92
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_trajectoryMeasure_explicitPolynomialPrefixAverageRealizedBehaviorRegretViolationSet_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability.lean:124
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.eventually_explicitPolynomialPrefixAverageRealizedBehaviorRegretUpperTailProbability_le_failureBudget theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability.lean:157
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixAverageRealizedBehaviorRegretUpperTailProbability_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability.lean:192
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_explicitPolynomialPrefixAverageRealizedBehaviorRegretUpperTailInProbability theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalRealizedBehaviorRegretUpperTailInProbability.lean:225
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalFirstPassageThreshold definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:38
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalFirstPassageThreshold_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:44
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalFirstPassageThreshold_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:56
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageStoppingPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:66
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayedSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:85
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayedProbability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:104
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayRate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:120
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayedSet_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:130
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayedSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:222
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayedSet_subset_distanceViolationSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:242
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayRate_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:282
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.explicitPolynomialPrefixExpectedAbsoluteAverageRealizedBehaviorRegret_div_reciprocalFirstPassageThreshold_le_delayRate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:307
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayRate_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:344
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayedProbability_le_rate theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:394
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageDelayedProbability_tendsto_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:466
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_reciprocalThresholdCappedDoubleLinearRawWindowFirstPassage_vanishingDelayProbability_and_L1_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalReciprocalThresholdCappedDoubleLinearRawWindowFirstPassageVanishingDelayProbabilityAndL1Consistency.lean:500
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalTrajectoryFiltration definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:39
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalTrajectoryFiltration_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:54
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalTrajectory_coordinate_of_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:70
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalSuccessorBatchAverageRealizedRegret_naturalTrajectoryFiltration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:105
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalCumulativeRealizedBehaviorRegret_naturalTrajectoryFiltration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:125
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.measurable_naturalAverageRealizedBehaviorRegret_naturalTrajectoryFiltration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:147
BanditRLProof.FiniteHorizonRL.HeterogeneousAdaptiveStochasticEpisodeBatchSource.naturalAverageRealizedBehaviorRegret_stronglyAdapted_naturalTrajectoryFiltration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:166
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalTrajectoryFiltration definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:184
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalAverageRealizedBehaviorRegretProcess_stronglyAdapted theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:201
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageRealizedBehaviorRegretProcess definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:222
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalStoppingTimeAverageRealizedBehaviorRegretProcess_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:246
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalStoppingTimeAverageRealizedBehaviorRegretProcess theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:272
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_stoppingTimeNaturalAverageRealizedBehaviorRegret_tendstoAlmostEverywhere_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:313
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_stoppingTimeNaturalAverageRealizedBehaviorRegret_tendstoAlmostEverywhere_zero_of_nat_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalStoppingTimeAverageRealizedBehaviorRegretAlmostSureConsistency.lean:385
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalThresholdTriggeredDoubleLinearRawWindowEarlyStopSet definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:35
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingPrefix definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:56
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingPrefix_eq_base_of_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:80
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingPrefix_eq_right_of_lt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:105
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurableSet_selfConsistentScheduledNaturalCausalThresholdTriggeredDoubleLinearRawWindowEarlyStopSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:136
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingPrefix_isStoppingTime theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:173
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingPrefix_lower theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:210
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingPrefix_upper theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:233
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_thresholdTriggeredDoubleLinearRawWindowStoppingTimeNaturalAverageRealizedBehaviorRegret_L1_consistency theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency Compiled BanditRLProof/RL/FiniteHorizonNaturalCausalThresholdTriggeredDoubleLinearRawWindowStoppingTimeL1AverageRealizedBehaviorRegretConsistency.lean:260
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stateOccupancy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:31
BanditRLProof.FiniteHorizonRL.MarkovPolicy.policyBellmanGap definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:61
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurable_policyBellmanGap theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:69
BanditRLProof.FiniteHorizonRL.MarkovPolicy.policyBellmanGap_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:79
BanditRLProof.FiniteHorizonRL.MarkovPolicy.policyBellmanGap_stageOfRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:92
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integral_inducedStateKernel_eq_integral_transitionValue theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:113
BanditRLProof.FiniteHorizonRL.MarkovPolicy.bellman_sub_bellman_eq_integral_inducedStateKernel_sub theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:134
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integral_sub_comp_inducedStateKernel_eq_integral_bellman_sub theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:186
BanditRLProof.FiniteHorizonRL.MarkovPolicy.occupancyGapRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:214
BanditRLProof.FiniteHorizonRL.MarkovPolicy.occupancyGapRemaining_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:231
BanditRLProof.FiniteHorizonRL.MarkovPolicy.occupancyGapRemaining_eq_integral_optimalValueRemaining_sub_valueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:248
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueRemaining_le_optimalValueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:291
BanditRLProof.FiniteHorizonRL.MarkovPolicy.occupancyGapRemaining_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:311
BanditRLProof.FiniteHorizonRL.MarkovPolicy.expectedRegret definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:323
BanditRLProof.FiniteHorizonRL.MarkovPolicy.expectedRegret_eq_integral_optimalValueAt_sub_valueAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:331
BanditRLProof.FiniteHorizonRL.MarkovPolicy.expectedRegret_eq_occupancyGapRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:351
BanditRLProof.FiniteHorizonRL.MarkovPolicy.expectedRegret_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:361
BanditRLProof.FiniteHorizonRL.MDP.optimalPolicy_expectedRegret_eq_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:373
BanditRLProof.FiniteHorizonRL.MDP.expectedRegret_eq_occupancyGap_nonneg_and_optimalPolicy_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOccupancyRegret Compiled BanditRLProof/RL/FiniteHorizonOccupancyRegret.lean:386
BanditRLProof.FiniteHorizonRL.MDP.optimalAction definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:27
BanditRLProof.FiniteHorizonRL.MDP.bellmanQ_le_optimalAction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:34
BanditRLProof.FiniteHorizonRL.MDP.measurable_optimalAction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:43
BanditRLProof.FiniteHorizonRL.MDP.optimalBellman definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:49
BanditRLProof.FiniteHorizonRL.MDP.bellmanQ_le_optimalBellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:55
BanditRLProof.FiniteHorizonRL.MDP.measurable_optimalBellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:62
BanditRLProof.FiniteHorizonRL.MDP.transitionValue_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:69
BanditRLProof.FiniteHorizonRL.MDP.bellmanQ_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:83
BanditRLProof.FiniteHorizonRL.MDP.optimalValueRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:92
BanditRLProof.FiniteHorizonRL.MDP.measurable_optimalValueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:100
BanditRLProof.FiniteHorizonRL.MDP.optimalValueAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:107
BanditRLProof.FiniteHorizonRL.MDP.measurable_optimalValueAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:112
BanditRLProof.FiniteHorizonRL.MDP.optimalValueRemaining_eq_of_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:120
BanditRLProof.FiniteHorizonRL.MDP.optimalValueAt_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:132
BanditRLProof.FiniteHorizonRL.MDP.optimalValueAt_bellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:144
BanditRLProof.FiniteHorizonRL.MarkovPolicy.bellman_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:172
BanditRLProof.FiniteHorizonRL.MarkovPolicy.bellman_le_optimalBellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:192
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueAt_le_optimalValueAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:213
BanditRLProof.FiniteHorizonRL.MDP.optimalPolicy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:241
BanditRLProof.FiniteHorizonRL.MDP.optimalPolicy_bellman_eq_optimalBellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:252
BanditRLProof.FiniteHorizonRL.MDP.optimalPolicy_valueAt_eq_optimalValueAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:269
BanditRLProof.FiniteHorizonRL.MDP.optimalValueAt_dominates_and_is_attained theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimality Compiled BanditRLProof/RL/FiniteHorizonOptimality.lean:298
BanditRLProof.FiniteHorizonRL.MDP.optimalBellman_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:31
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:47
BanditRLProof.FiniteHorizonRL.MDP.optimalBellmanCertificate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:60
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.measurable_upperValueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:71
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.optimalValueRemaining_le_upperValueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:78
BanditRLProof.FiniteHorizonRL.MarkovPolicy.occupancySumRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:105
BanditRLProof.FiniteHorizonRL.MarkovPolicy.occupancySumRemaining_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:120
BanditRLProof.FiniteHorizonRL.MarkovPolicy.occupancySumRemaining_mono theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:135
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.policyBellmanResidual definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:169
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.measurable_policyBellmanResidual theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:178
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.policyBellmanResidual_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:188
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.residualOccupancyRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:203
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.residualOccupancyRemaining_eq_integral_upperValueRemaining_sub_valueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:214
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.optimalBellmanCertificate_residualOccupancyRemaining_eq_occupancyGapRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:266
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.residualOccupancyRemaining_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:278
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.expectedRegret_le_residualOccupancyRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:294
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.residualOccupancyRemaining_le_occupancySumRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:313
BanditRLProof.FiniteHorizonRL.MDP.OptimisticBellmanCertificate.expectedRegret_le_residual_le_occupancyBonusRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonOptimisticCertificate Compiled BanditRLProof/RL/FiniteHorizonOptimisticCertificate.lean:334
BanditRLProof.FiniteHorizonRL.MarkovPolicy structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:27
BanditRLProof.FiniteHorizonRL.MarkovPolicy.inducedStateKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:42
BanditRLProof.FiniteHorizonRL.MarkovPolicy.bellman definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:57
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurable_bellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:65
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:77
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurable_valueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:87
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:99
BanditRLProof.FiniteHorizonRL.MarkovPolicy.measurable_valueAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:105
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueRemaining_eq_of_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:112
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueAt_horizon theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:123
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueAt_bellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonPolicy Compiled BanditRLProof/RL/FiniteHorizonPolicy.lean:138
BanditRLProof.FiniteHorizonRL.StepTrace.stateAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:24
BanditRLProof.FiniteHorizonRL.StepTrace.stateAt_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:30
BanditRLProof.FiniteHorizonRL.StepTrace.stateAt_zero_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:36
BanditRLProof.FiniteHorizonRL.StepTrace.stateAt_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:42
BanditRLProof.FiniteHorizonRL.StepTrace.stateAt_eq_if theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:53
BanditRLProof.FiniteHorizonRL.StepTrace.stateActionAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:67
BanditRLProof.FiniteHorizonRL.StepTrace.stateActionNextAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:71
BanditRLProof.FiniteHorizonRL.StepTrace.stateActionAt_cons_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:77
BanditRLProof.FiniteHorizonRL.StepTrace.stateActionNextAt_cons_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:84
BanditRLProof.FiniteHorizonRL.StepTrace.measurable_stateActionAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:94
BanditRLProof.FiniteHorizonRL.StepTrace.measurable_stateActionNextAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:99
BanditRLProof.FiniteHorizonRL.MDP.stepTrace_stateAt_eq_trajectoryStateAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:112
BanditRLProof.FiniteHorizonRL.MarkovPolicy.actionStateKernel_apply_singleton theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:128
BanditRLProof.FiniteHorizonRL.MarkovPolicy.actionStateKernel_apply_actionSet theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:143
BanditRLProof.FiniteHorizonRL.MarkovPolicy.trajectoryKernelRemaining_map_head theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:154
BanditRLProof.FiniteHorizonRL.MarkovPolicy.trajectoryKernelRemaining_transitionEvent_eq_visitEvent_mul theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:170
BanditRLProof.FiniteHorizonRL.MarkovPolicy.trajectoryMeasure_transitionEvent_eq_visitEvent_mul theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:260
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageTransitionJointProbability_eq_stageVisitProbability_mul_transition theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageTransitionJointFactorization Compiled BanditRLProof/RL/FiniteHorizonStageTransitionJointFactorization.lean:291
BanditRLProof.FiniteHorizonRL.MDP.stageOfRemainingCoordinate definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageVisitFactorization Compiled BanditRLProof/RL/FiniteHorizonStageVisitFactorization.lean:28
BanditRLProof.FiniteHorizonRL.MDP.stageOfRemainingCoordinate_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageVisitFactorization Compiled BanditRLProof/RL/FiniteHorizonStageVisitFactorization.lean:36
BanditRLProof.FiniteHorizonRL.MDP.stageOfRemainingCoordinate_full theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageVisitFactorization Compiled BanditRLProof/RL/FiniteHorizonStageVisitFactorization.lean:48
BanditRLProof.FiniteHorizonRL.MarkovPolicy.trajectoryKernelRemaining_visitEvent_eq_stateEvent_mul_action theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageVisitFactorization Compiled BanditRLProof/RL/FiniteHorizonStageVisitFactorization.lean:64
BanditRLProof.FiniteHorizonRL.MarkovPolicy.trajectoryMeasure_visitEvent_eq_stateEvent_mul_action theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageVisitFactorization Compiled BanditRLProof/RL/FiniteHorizonStageVisitFactorization.lean:140
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageStateProbability definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageVisitFactorization Compiled BanditRLProof/RL/FiniteHorizonStageVisitFactorization.lean:186
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stageVisitProbability_eq_stageStateProbability_mul_action theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStageVisitFactorization Compiled BanditRLProof/RL/FiniteHorizonStageVisitFactorization.lean:194
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:39
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardNextStateKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:54
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticBellmanQ definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:66
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.integrable_reward_add_value theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:73
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticBellmanQ_eq_bellmanQ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:92
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticBellman definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:126
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticBellman_eq_bellman theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:134
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticValueRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:147
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticValueRemaining_eq_valueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:158
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticValueAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:176
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticValueAt_eq_valueAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:184
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.deterministic definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:193
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.meanPlanningTransport theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellman Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellman.lean:213
BanditRLProof.Concentration.intervalVarianceProxy_neg_coe theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:20
BanditRLProof.FiniteHorizonRL.meanBellmanInnovationStepVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:34
BanditRLProof.FiniteHorizonRL.meanBellmanInnovationVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:39
BanditRLProof.FiniteHorizonRL.meanBellmanInnovationVarianceProxy_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:45
BanditRLProof.FiniteHorizonRL.meanBellmanInnovationVarianceProxy_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:49
BanditRLProof.FiniteHorizonRL.meanBellmanInnovationVarianceProxy_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:56
BanditRLProof.FiniteHorizonRL.MarkovPolicy.valueRemaining_abs_le_of_rewardBound theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:70
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeMeanBellmanInnovationFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:122
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeMeanBellmanInnovationFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:135
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardStateKernel_map_dropReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:173
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.integral_meanBellmanReturn_actionStateKernel_eq_valueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:204
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionStateKernel_meanBellmanInnovation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:244
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardStateKernel_meanBellmanInnovation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:296
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_sampledCumulativeMeanBellmanInnovationFrom_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:361
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_sampledCumulativeMeanBellmanInnovationFrom_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardBellmanInnovationConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardBellmanInnovationConcentration.lean:594
BanditRLProof.FiniteHorizonRL.MDP.headRewardMean definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:30
BanditRLProof.FiniteHorizonRL.MDP.measurable_headRewardMean theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:37
BanditRLProof.FiniteHorizonRL.MDP.measurable_headRewardMean_comap_headAction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:45
BanditRLProof.FiniteHorizonRL.MDP.headRewardDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:59
BanditRLProof.FiniteHorizonRL.MDP.measurable_headRewardDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:67
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.UniformSubgaussianRewardLaw structure Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:78
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.uniformSubgaussianRewardLaw_of_mem_Icc theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:87
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_headRewardDeviation_hasCondSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:106
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_headRewardDeviation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:162
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_headRewardDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConcentration.lean:200
BanditRLProof.FiniteHorizonRL.RewardStepTrace.headAction definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConditionalLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConditionalLaw.lean:30
BanditRLProof.FiniteHorizonRL.RewardStepTrace.measurable_headAction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConditionalLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConditionalLaw.lean:35
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.selectedRewardKernelAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConditionalLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConditionalLaw.lean:46
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardKernel_eq_compProd_selectedRewardKernelAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConditionalLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConditionalLaw.lean:59
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardKernel_map_fst theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConditionalLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConditionalLaw.lean:73
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_map_headAction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConditionalLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConditionalLaw.lean:86
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardKernel_condDistrib_reward_given_action theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConditionalLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConditionalLaw.lean:115
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_condDistrib_headReward_given_headAction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConditionalLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConditionalLaw.lean:136
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_condExpKernel_map_headReward_given_headAction theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardConditionalLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardConditionalLaw.lean:179
BanditRLProof.Concentration.kernel_hasSubgaussianMGF_of_ae theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardCumulativeConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardCumulativeConcentration.lean:21
BanditRLProof.Concentration.hasSubgaussianMGF_apply_of_kernel_dirac theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardCumulativeConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardCumulativeConcentration.lean:57
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeRewardDeviationFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardCumulativeConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardCumulativeConcentration.lean:88
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeRewardDeviationFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardCumulativeConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardCumulativeConcentration.lean:96
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardStateKernel_rewardDeviation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardCumulativeConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardCumulativeConcentration.lean:123
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_sampledCumulativeRewardDeviationFrom_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardCumulativeConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardCumulativeConcentration.lean:161
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_sampledCumulativeRewardDeviationFrom_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardCumulativeConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardCumulativeConcentration.lean:344
BanditRLProof.FiniteHorizonRL.RewardStepTrace.eraseRewards definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:34
BanditRLProof.FiniteHorizonRL.RewardStepTrace.measurable_eraseRewards theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:40
BanditRLProof.FiniteHorizonRL.RewardStepTrace.eraseRewards_cons theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:51
BanditRLProof.FiniteHorizonRL.ProbabilityTheory.compProd_map_prodMap_of_map_eq theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:70
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_map_eraseRewards theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:130
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.eraseTrajectory definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:235
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_eraseTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:241
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryMeasure_map_eraseTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:247
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.eraseTrajectoryFamily definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:267
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_eraseTrajectoryFamily theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:274
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_map_eraseTrajectoryFamily theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:282
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.knownRewardEpisodeBatchOfStochasticTrajectories definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:312
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_knownRewardEpisodeBatchOfStochasticTrajectories theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:322
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_map_knownRewardEpisodeBatch_eq_iidEpisodeBatchMeasure theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardErasureLaw Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardErasureLaw.lean:335
BanditRLProof.FiniteHorizonRL.MDP.rewardStepTrace_stateAt_eq_trajectoryStateAt_eraseTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:30
BanditRLProof.FiniteHorizonRL.MDP.sampledEpisodeStep_state_eq_knownRewardEpisodeStep theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:43
BanditRLProof.FiniteHorizonRL.MDP.sampledEpisodeStep_action_eq_knownRewardEpisodeStep theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:56
BanditRLProof.FiniteHorizonRL.MDP.sampledEpisodeStep_nextState_eq_knownRewardEpisodeStep theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:68
BanditRLProof.FiniteHorizonRL.MDP.sampledEpisodeBatch_visitCount_eq_knownRewardEpisodeBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:79
BanditRLProof.FiniteHorizonRL.MDP.sampledEpisodeBatch_transitionCount_eq_knownRewardEpisodeBatch theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:111
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticSampledBatchCountBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:161
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.mem_stochasticSampledBatchCountBadEvent_iff_knownReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:171
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurableSet_stochasticSampledBatchCountBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:211
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_stochasticSampledBatchCountBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:223
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.simultaneousRewardDelta definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:259
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.simultaneousRewardSumConfidenceRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:264
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardCoordinateBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:272
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.simultaneousRewardBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:284
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurableSet_rewardCoordinateBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:292
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurableSet_simultaneousRewardBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:309
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.simultaneousRewardDelta_pos theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:320
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.simultaneousRewardDelta_le_one theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:329
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_simultaneousRewardBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:340
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.maskedRewardDeviation_sum_abs_lt_of_not_mem_simultaneousRewardBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:390
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.maskedRewardDeviation_sum_eq_sampledBatch_rewardSum_sub theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:408
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.expectedCountRewardCoordinateRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:443
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.sampledBatch_empiricalReward_abs_sub_le_expectedCountRewardCoordinateRadius theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:454
BanditRLProof.FiniteHorizonRL.stochasticEmpiricalFiniteBatchValueEnvelope definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:539
BanditRLProof.FiniteHorizonRL.MDP.stochasticAllCoordinateEmpiricalFiniteBatchModel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:548
BanditRLProof.FiniteHorizonRL.MDP.StochasticAllCoordinateConfidence.upperValueRemaining_abs_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:565
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stochasticAllCoordinateEmpiricalFiniteBatchModelConfidence_of_not_mem definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:680
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticAllCoordinateEmpiricalModelBadEvent definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:787
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurableSet_stochasticAllCoordinateEmpiricalModelBadEvent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:799
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_stochasticAllCoordinateEmpiricalModelBadEvent_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:814
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidStochasticTrajectoryFamilyMeasure_allCoordinate_finiteBatchModel_confidence theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:848
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidStochasticTrajectoryFamilyMeasure_allCoordinate_optimism_and_expectedRegret theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDAllCoordinateEmpiricalModelConfidence.lean:923
BanditRLProof.Concentration.hasSubgaussianMGF_compProd_of_forall theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:26
BanditRLProof.Concentration.hasSubgaussianMGF_zero_of_proxy theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:108
BanditRLProof.FiniteHorizonRL.RewardStepTrace.stateAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:133
BanditRLProof.FiniteHorizonRL.RewardStepTrace.measurable_stateAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:143
BanditRLProof.FiniteHorizonRL.RewardStepTrace.stateAt_cons_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:156
BanditRLProof.FiniteHorizonRL.RewardStepTrace.stateAt_cons_succ theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:168
BanditRLProof.FiniteHorizonRL.RewardStepTrace.measurable_stateAt_prod theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:203
BanditRLProof.FiniteHorizonRL.MDP.maskedRewardDeviationAt definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:217
BanditRLProof.FiniteHorizonRL.MDP.measurable_maskedRewardDeviationAt theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:227
BanditRLProof.FiniteHorizonRL.MDP.measurable_maskedRewardDeviationAt_trajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:243
BanditRLProof.FiniteHorizonRL.MDP.sampledEpisodeStepOfStochasticTrajectory definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:262
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledEpisodeStepOfStochasticTrajectory theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:271
BanditRLProof.FiniteHorizonRL.MDP.sampledEpisodeBatchOfStochasticTrajectories definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:293
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledEpisodeBatchOfStochasticTrajectories theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:302
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardStateKernel_maskedRewardDeviation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:319
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_maskedRewardDeviationAt_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:371
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryMeasure_maskedRewardDeviationAt_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:454
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.maskedRewardDeviationAtEpisode definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:482
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iIndepFun_maskedRewardDeviationAtEpisode theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:491
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.maskedRewardDeviationAtEpisode_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:508
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_maskedRewardDeviation_sum_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:537
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_maskedRewardDeviation_sum_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDEmpiricalRewardConfidence.lean:561
BanditRLProof.FiniteHorizonRL.uniformFloorStochasticRewardCoordinateRadius definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDExplicitCalibration.lean:28
BanditRLProof.FiniteHorizonRL.uniformFloorStochasticRewardCoordinateRadius_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDExplicitCalibration.lean:40
BanditRLProof.FiniteHorizonRL.uniformFloorStochasticTransitionBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDExplicitCalibration.lean:53
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.expectedCountRewardCoordinateRadius_le_uniformFloor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDExplicitCalibration.lean:64
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stochasticTransitionCover_of_uniformExpectedCountFloor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDExplicitCalibration.lean:108
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidStochasticTrajectoryFamilyMeasure_allCoordinate_optimism_and_expectedRegret_of_uniformExpectedCountFloor theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDExplicitCalibration.lean:211
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryPolicy_iidStochasticTrajectoryFamilyMeasure_allCoordinate_optimism_and_expectedRegret_of_pathSupport_explicitCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDExplicitCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDExplicitCalibration.lean:307
BanditRLProof.FiniteHorizonRL.selfConsistentTransitionBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:20
BanditRLProof.FiniteHorizonRL.selfConsistentTransitionBudget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:25
BanditRLProof.FiniteHorizonRL.selfConsistentTransitionBudget_fixedPoint theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:33
BanditRLProof.FiniteHorizonRL.uniformFloorStochasticTransitionContraction definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:50
BanditRLProof.FiniteHorizonRL.uniformFloorStochasticTransitionContraction_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:61
BanditRLProof.FiniteHorizonRL.uniformFloorStochasticSelfConsistentTransitionBudget definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:75
BanditRLProof.FiniteHorizonRL.uniformFloorStochasticSelfConsistentTransitionBudget_nonneg theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:87
BanditRLProof.FiniteHorizonRL.uniformFloorStochasticSelfConsistentTransitionBudget_fixedPoint theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:108
BanditRLProof.FiniteHorizonRL.MarkovPolicy.stochasticTransitionCover_of_uniformExpectedCountFloor_selfConsistent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:131
BanditRLProof.FiniteHorizonRL.MarkovPolicy.iidStochasticTrajectoryFamilyMeasure_allCoordinate_optimism_and_expectedRegret_of_uniformExpectedCountFloor_selfConsistent theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:242
BanditRLProof.FiniteHorizonRL.DeterministicMarkovPolicyTable.exploratoryPolicy_iidStochasticTrajectoryFamilyMeasure_allCoordinate_optimism_and_expectedRegret_of_pathSupport_selfConsistentCalibration theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDSelfConsistentCalibration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDSelfConsistentCalibration.lean:333
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeReturnDeviationAtEpisode definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:28
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeReturnDeviationAtEpisode theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:36
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeReturnDeviationSum definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:44
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeReturnDeviationSum theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:53
BanditRLProof.FiniteHorizonRL.MDP.iidSampledCumulativeReturnDeviationVarianceProxy definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:61
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:76
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_map_eval theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:96
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iIndepFun_sampledCumulativeReturnDeviationAtEpisode theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:111
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.sampledCumulativeReturnDeviationAtEpisode_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:126
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_sampledCumulativeReturnDeviationSum_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:160
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.iidStochasticTrajectoryFamilyMeasure_sampledCumulativeReturnDeviationSum_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardIIDTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardIIDTotalReturnConcentration.lean:193
BanditRLProof.Concentration.hasSubgaussianMGF_compProd_of_forall_fintype theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration.lean:25
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeReturnDeviation definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration.lean:91
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeReturnDeviation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration.lean:98
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryMeasure_sampledCumulativeReturnDeviation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration.lean:112
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryMeasure_sampledCumulativeReturnDeviation_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardInitialLawTotalReturnConcentration.lean:142
BanditRLProof.FiniteHorizonRL.RewardStepTrace.head definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:27
BanditRLProof.FiniteHorizonRL.RewardStepTrace.measurable_head theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:33
BanditRLProof.FiniteHorizonRL.RewardStepTrace.headActionReward definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:39
BanditRLProof.FiniteHorizonRL.RewardStepTrace.measurable_headActionReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:44
BanditRLProof.FiniteHorizonRL.RewardStepTrace.headReward definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:53
BanditRLProof.FiniteHorizonRL.RewardStepTrace.measurable_headReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:58
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:69
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardMarginalKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:86
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_map_head theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:102
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_map_headActionReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:124
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_map_headReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:157
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardKernel_apply_prod theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:187
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardMarginalKernel_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:217
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_headMarginalFactorization theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardMarginal Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardMarginal.lean:243
ProbabilityTheory.Kernel.compProd_prodMkRight_eq_prod theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:27
ProbabilityTheory.Kernel.map_compProd_prodMk theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:39
BanditRLProof.FiniteHorizonRL.MarkovPolicy.retainedActionStateKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:79
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeReturnDeviationFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:98
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeReturnDeviationFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:106
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeReturnDeviationFrom_eq_rewardDeviation_add_meanBellmanInnovation theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:120
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardDeviationAfterActionState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:147
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_rewardDeviationAfterActionState theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:151
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rawRewardKernelAfterActionState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:158
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardDeviationKernelAfterActionState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:175
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardDeviationKernelAfterActionState_apply theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:191
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardDeviationKernelAfterActionState_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:209
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rawRewardKernelAfterRetainedActionState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:236
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardDeviationKernelAfterRetainedActionState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:243
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.uncenterRewardAfterRetainedActionState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:264
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_uncenterRewardAfterRetainedActionState theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:268
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.rewardDeviationKernelAfterRetainedActionState_map_uncenter theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:276
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.retainedActionStateKernel_compProd_rewardDeviation_map_uncenter theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:300
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.assembleRawRewardAfterRetainedActionState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:320
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_assembleRawRewardAfterRetainedActionState theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:326
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.retainedActionStateKernel_compProd_rawReward_map_assemble theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:334
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.assembleRewardDeviationAfterRetainedActionState definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:408
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_assembleRewardDeviationAfterRetainedActionState theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:414
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.retainedActionStateKernel_compProd_rewardDeviation_map_assemble theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:423
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.retainedActionStateKernel_meanBellmanInnovation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:451
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardStateKernel_sampledReturnBellmanInnovation_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:513
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_sampledCumulativeReturnDeviationFrom_hasSubgaussianMGF theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:622
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining_sampledCumulativeReturnDeviationFrom_abs_tail_le theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTotalReturnConcentration Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTotalReturnConcentration.lean:877
BanditRLProof.FiniteHorizonRL.RewardStepTrace abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:26
BanditRLProof.FiniteHorizonRL.RewardStepTrace.measurable_cons theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:33
BanditRLProof.FiniteHorizonRL.RewardStepTrace.measurable_tail theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:45
BanditRLProof.FiniteHorizonRL.integrable_of_fintype_aestronglyMeasurable theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:55
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.actionRewardStateKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:72
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryKernelRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:92
BanditRLProof.FiniteHorizonRL.MDP.sampledCumulativeRewardFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:134
BanditRLProof.FiniteHorizonRL.MDP.measurable_sampledCumulativeRewardFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:142
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.integrable_sampledCumulativeRewardFrom_stochasticTrajectoryKernelRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:165
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.integral_sampledCumulativeRewardFrom_stochasticTrajectoryKernelRemaining_eq_stochasticValueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:312
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.stochasticTrajectoryMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:400
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.sampledCumulativeReward definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:416
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.measurable_sampledCumulativeReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:421
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.integrable_sampledCumulativeReward_stochasticTrajectoryMeasure theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:426
BanditRLProof.FiniteHorizonRL.MDP.MeanCompatibleRewardKernel.integral_sampledCumulativeReward_stochasticTrajectoryMeasure_eq_integral_valueAt_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonStochasticRewardTrajectory Compiled BanditRLProof/RL/FiniteHorizonStochasticRewardTrajectory.lean:455
BanditRLProof.FiniteHorizonRL.StepTrace abbreviation Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:25
BanditRLProof.FiniteHorizonRL.StepTrace.measurable_cons theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:32
BanditRLProof.FiniteHorizonRL.StepTrace.measurable_tail theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:43
BanditRLProof.FiniteHorizonRL.integrable_of_fintype theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:53
BanditRLProof.FiniteHorizonRL.MarkovPolicy.actionStateKernel definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:67
BanditRLProof.FiniteHorizonRL.MarkovPolicy.trajectoryKernelRemaining definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:85
BanditRLProof.FiniteHorizonRL.MDP.cumulativeRewardFrom definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:125
BanditRLProof.FiniteHorizonRL.MDP.measurable_cumulativeRewardFrom theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:133
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integrable_cumulativeRewardFrom_trajectoryKernelRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:157
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integral_cumulativeRewardFrom_trajectoryKernelRemaining_eq_valueRemaining theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:171
BanditRLProof.FiniteHorizonRL.MarkovPolicy.trajectoryMeasure definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:263
BanditRLProof.FiniteHorizonRL.MDP.cumulativeReward definition Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:282
BanditRLProof.FiniteHorizonRL.MDP.measurable_cumulativeReward theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:287
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integrable_cumulativeReward_trajectoryMeasure theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:296
BanditRLProof.FiniteHorizonRL.MarkovPolicy.integral_cumulativeReward_trajectoryMeasure_eq_integral_valueAt_zero theorem Finite-horizon RL BanditRLProof.RL.FiniteHorizonTrajectory Compiled BanditRLProof/RL/FiniteHorizonTrajectory.lean:307
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointError definition Finite-horizon RL BanditRLProof.RL.StoppedReturnJointErrorDeterministicTailHighProbability Compiled BanditRLProof/RL/StoppedReturnJointErrorDeterministicTailHighProbability.lean:34
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointError_nonneg theorem Finite-horizon RL BanditRLProof.RL.StoppedReturnJointErrorDeterministicTailHighProbability Compiled BanditRLProof/RL/StoppedReturnJointErrorDeterministicTailHighProbability.lean:95
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.measurable_selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointError theorem Finite-horizon RL BanditRLProof.RL.StoppedReturnJointErrorDeterministicTailHighProbability Compiled BanditRLProof/RL/StoppedReturnJointErrorDeterministicTailHighProbability.lean:116
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointError_lt_iff theorem Finite-horizon RL BanditRLProof.RL.StoppedReturnJointErrorDeterministicTailHighProbability Compiled BanditRLProof/RL/StoppedReturnJointErrorDeterministicTailHighProbability.lean:179
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointViolationSet_eq_jointError_ge theorem Finite-horizon RL BanditRLProof.RL.StoppedReturnJointErrorDeterministicTailHighProbability Compiled BanditRLProof/RL/StoppedReturnJointErrorDeterministicTailHighProbability.lean:242
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledNaturalCausalInverseSqrtThresholdCappedUnboundedHittingAfterStoppedReturnJointGoodSet_eq_jointError_lt theorem Finite-horizon RL BanditRLProof.RL.StoppedReturnJointErrorDeterministicTailHighProbability Compiled BanditRLProof/RL/StoppedReturnJointErrorDeterministicTailHighProbability.lean:266
BanditRLProof.FiniteHorizonRL.AdaptiveStochasticSampledEmpiricalOptimisticSource.selfConsistentScheduledCausalSource_inverseSqrtThresholdCappedUnboundedHittingAfter_stoppedSampledReturn_and_successorPolicyExpectedReturn_jointError_deterministicTailHighProbability_optimality theorem Finite-horizon RL BanditRLProof.RL.StoppedReturnJointErrorDeterministicTailHighProbability Compiled BanditRLProof/RL/StoppedReturnJointErrorDeterministicTailHighProbability.lean:293
BanditRLProof.measurable_rat_div_const theorem Foundations BanditRLProof.RatMeasurability Compiled BanditRLProof/RatMeasurability.lean:21
BanditRLProof.realKernelMean definition Foundations BanditRLProof.RealKernelRegretPullCount Compiled BanditRLProof/RealKernelRegretPullCount.lean:20
BanditRLProof.realKernelGap definition Foundations BanditRLProof.RealKernelRegretPullCount Compiled BanditRLProof/RealKernelRegretPullCount.lean:25
BanditRLProof.realKernelRegret definition Foundations BanditRLProof.RealKernelRegretPullCount Compiled BanditRLProof/RealKernelRegretPullCount.lean:30
BanditRLProof.realKernelGap_nonneg theorem Foundations BanditRLProof.RealKernelRegretPullCount Compiled BanditRLProof/RealKernelRegretPullCount.lean:36
BanditRLProof.realKernelRegret_eq_finset_sum_gap theorem Foundations BanditRLProof.RealKernelRegretPullCount Compiled BanditRLProof/RealKernelRegretPullCount.lean:44
BanditRLProof.realKernelRegret_eq_sum_gap_mul_pullCount theorem Foundations BanditRLProof.RealKernelRegretPullCount Compiled BanditRLProof/RealKernelRegretPullCount.lean:54
BanditRLProof.integrable_realKernelRegret_of_integrable_pullCount theorem Foundations BanditRLProof.RealKernelRegretPullCount Compiled BanditRLProof/RealKernelRegretPullCount.lean:65
BanditRLProof.integral_realKernelRegret_eq_sum_gap_mul_integral_pullCount theorem Foundations BanditRLProof.RealKernelRegretPullCount Compiled BanditRLProof/RealKernelRegretPullCount.lean:88
BanditRLProof.realMeanGap definition Foundations BanditRLProof.RealMeanRegretPullCount Compiled BanditRLProof/RealMeanRegretPullCount.lean:22
BanditRLProof.realMeanRegret definition Foundations BanditRLProof.RealMeanRegretPullCount Compiled BanditRLProof/RealMeanRegretPullCount.lean:26
BanditRLProof.realMeanRegret_eq_finset_sum_gap theorem Foundations BanditRLProof.RealMeanRegretPullCount Compiled BanditRLProof/RealMeanRegretPullCount.lean:32
BanditRLProof.realMeanRegret_eq_sum_gap_mul_pullCount theorem Foundations BanditRLProof.RealMeanRegretPullCount Compiled BanditRLProof/RealMeanRegretPullCount.lean:48
BanditRLProof.integrable_realMeanRegret_of_integrable_pullCount theorem Foundations BanditRLProof.RealMeanRegretPullCount Compiled BanditRLProof/RealMeanRegretPullCount.lean:70
BanditRLProof.integral_realMeanRegret_eq_sum_gap_mul_integral_pullCount theorem Foundations BanditRLProof.RealMeanRegretPullCount Compiled BanditRLProof/RealMeanRegretPullCount.lean:106
BanditRLProof.pseudoRegret definition Foundations BanditRLProof.Regret Compiled BanditRLProof/Regret.lean:16
BanditRLProof.pseudoRegret_zero theorem Foundations BanditRLProof.Regret Compiled BanditRLProof/Regret.lean:21
BanditRLProof.pseudoRegret_succ theorem Foundations BanditRLProof.Regret Compiled BanditRLProof/Regret.lean:25
BanditRLProof.RegretBoundCard structure Foundations BanditRLProof.Regret Compiled BanditRLProof/Regret.lean:31
BanditRLProof.RegretObligation structure Foundations BanditRLProof.Regret Compiled BanditRLProof/Regret.lean:41
BanditRLProof.pseudoRegret_le_finset_sum_gap_mul_count_bound theorem Foundations BanditRLProof.RegretCountBounds Compiled BanditRLProof/RegretCountBounds.lean:26
BanditRLProof.pseudoRegret_le_finset_sum_gap_mul_nat_count_bound theorem Foundations BanditRLProof.RegretCountBounds Compiled BanditRLProof/RegretCountBounds.lean:52
BanditRLProof.pseudoRegret_le_sum_gap_mul_uniform_nat_count_bound theorem Foundations BanditRLProof.RegretCountBounds Compiled BanditRLProof/RegretCountBounds.lean:80
BanditRLProof.pseudoRegret_eq_finset_sum_gap_mul_pullCount theorem Foundations BanditRLProof.RegretDecomposition Compiled BanditRLProof/RegretDecomposition.lean:27
BanditRLProof.RewardKernel.MarkovRewardKernel structure Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:31
BanditRLProof.RewardKernel.ofKernel definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:46
BanditRLProof.RewardKernel.measurable_kernel theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:54
BanditRLProof.RewardKernel.measurable_apply_of_measurable_index theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:60
BanditRLProof.RewardKernel.measurable_eventProbability_of_measurable_index theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:72
BanditRLProof.RewardKernel.isProbabilityMeasure_apply theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:85
BanditRLProof.RewardKernel.apply_univ theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:94
BanditRLProof.RewardKernel.const definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:103
BanditRLProof.RewardKernel.deterministic definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:113
BanditRLProof.RewardKernel.selectedMeasure definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:127
BanditRLProof.RewardKernel.contextIndependentOfActionLaws definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:138
BanditRLProof.RewardKernel.selectedMeasure_contextIndependentOfActionLaws theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:153
BanditRLProof.RewardKernel.isProbabilityMeasure_selectedMeasure theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:164
BanditRLProof.RewardKernel.selectedMeasure_univ theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:173
BanditRLProof.RewardKernel.measurable_selectedMeasure_of_measurable theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:183
BanditRLProof.RewardKernel.measurable_selectedEventProbability_of_measurable theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:202
BanditRLProof.RewardKernel.measurable_selectedMeasure_of_policy_state theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:224
BanditRLProof.RewardKernel.measurable_selectedEventProbability_of_policy_state theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:247
BanditRLProof.RewardKernel.policyContextStateIndex definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:273
BanditRLProof.RewardKernel.measurable_policyContextStateIndex theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:280
BanditRLProof.RewardKernel.composePolicy definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:294
BanditRLProof.RewardKernel.composePolicy_kernel_apply theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:315
BanditRLProof.RewardKernel.isMarkovKernel_composePolicy theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:325
BanditRLProof.RewardKernel.measurable_composePolicy_eventProbability theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:337
BanditRLProof.RewardKernel.policyActionOfContextState definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:358
BanditRLProof.RewardKernel.measurable_policyActionOfContextState theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:365
BanditRLProof.RewardKernel.policyActionKernel definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:372
BanditRLProof.RewardKernel.policyActionKernel_apply theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:381
BanditRLProof.RewardKernel.isMarkovKernel_policyActionKernel theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:390
BanditRLProof.RewardKernel.composePolicyActionReward definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:407
BanditRLProof.RewardKernel.composePolicyActionReward_kernel theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:428
BanditRLProof.RewardKernel.isMarkovKernel_composePolicyActionReward theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:439
BanditRLProof.RewardKernel.measurable_composePolicyActionReward_eventProbability theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:450
BanditRLProof.RewardKernel.composePolicyActionReward_reward_event theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:474
BanditRLProof.RewardKernel.composePolicyActionReward_reward_map theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:522
BanditRLProof.RewardKernel.composePolicyActionReward_kernel_apply_eq_map_prod_mk theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:541
BanditRLProof.RewardKernel.composePolicyActionReward_action_map theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:574
BanditRLProof.RewardKernel.CenteredRewardKernelLaw structure Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:630
BanditRLProof.RewardKernel.composePolicy_centeredReward_integrable theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:659
BanditRLProof.RewardKernel.composePolicy_centeredReward_integral_eq_zero theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:681
BanditRLProof.RewardKernel.composePolicy_centeredReward_hasSubgaussianMGF theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:702
BanditRLProof.RewardKernel.historyStepRewardKernel definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:729
BanditRLProof.RewardKernel.historyStepKernelFamily definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:760
BanditRLProof.RewardKernel.historyStepKernelFamily_apply theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:777
BanditRLProof.RewardKernel.isMarkovKernel_historyStepKernelFamily theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:795
BanditRLProof.RewardKernel.measurable_historyStepKernelFamily_eventProbability theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:834
BanditRLProof.RewardKernel.historyStepKernelFamily_centeredReward_integrable theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:860
BanditRLProof.RewardKernel.historyStepKernelFamily_centeredReward_integral_eq_zero theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:889
BanditRLProof.RewardKernel.historyStepKernelFamily_centeredReward_hasSubgaussianMGF theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:919
BanditRLProof.RewardKernel.partialTrajectoryKernel definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:955
BanditRLProof.RewardKernel.isMarkovKernel_partialTrajectoryKernel theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:976
BanditRLProof.RewardKernel.measurable_partialTrajectoryKernel_eventProbability theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1004
BanditRLProof.RewardKernel.partialTrajectoryKernel_succ_next_map theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1036
BanditRLProof.RewardKernel.partialTrajectoryKernel_succ_next_map_apply theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1068
BanditRLProof.RewardKernel.actionRewardHistoryStepKernel definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1107
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1144
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_apply theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1165
BanditRLProof.RewardKernel.isMarkovKernel_actionRewardHistoryStepKernelFamily theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1186
BanditRLProof.RewardKernel.measurable_actionRewardHistoryStepKernelFamily_eventProbability theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1232
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_reward_event theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1263
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_reward_map theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1297
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_action_map theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1329
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_apply_eq_map_prod_mk theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1358
BanditRLProof.RewardKernel.actionRewardPartialTrajectoryKernel definition Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1391
BanditRLProof.RewardKernel.isMarkovKernel_actionRewardPartialTrajectoryKernel theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1415
BanditRLProof.RewardKernel.measurable_actionRewardPartialTrajectoryKernel_eventProbability theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1446
BanditRLProof.RewardKernel.actionRewardPartialTrajectoryKernel_succ_next_map theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1480
BanditRLProof.RewardKernel.actionRewardPartialTrajectoryKernel_succ_next_map_apply theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1518
BanditRLProof.RewardKernel.actionRewardPartialTrajectoryKernel_succ_extend_map_apply theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1557
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_condDistrib_trajMeasure theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1640
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_reward_condDistrib_trajMeasure theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1691
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_action_condDistrib_trajMeasure theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1789
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_selectedAction_condDistrib_trajMeasure theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1885
BanditRLProof.RewardKernel.actionRewardHistoryStepKernelFamily_selectedMeasure_condDistrib_trajMeasure theorem Probability layer BanditRLProof.RewardKernel Compiled BanditRLProof/RewardKernel.lean:1941
BanditRLProof.RewardKernel.trajMeasure_map_eval_zero theorem Probability layer BanditRLProof.RewardTraceLaw Compiled BanditRLProof/RewardTraceLaw.lean:26
BanditRLProof.RewardKernel.rewardTrace_prefix_map_eq_trajMeasure_of_condDistrib theorem Probability layer BanditRLProof.RewardTraceLaw Compiled BanditRLProof/RewardTraceLaw.lean:70
BanditRLProof.RewardKernel.rewardTrace_map_eq_trajMeasure_of_condDistrib theorem Probability layer BanditRLProof.RewardTraceLaw Compiled BanditRLProof/RewardTraceLaw.lean:267
BanditRLProof.RewardKernel.identDistrib_rewardTrace_of_common_condDistrib theorem Probability layer BanditRLProof.RewardTraceLaw Compiled BanditRLProof/RewardTraceLaw.lean:347
BanditRLProof.ENNReal.ofReal_finset_sum_mul_natCast_of_nonneg theorem Foundations BanditRLProof.ScalarENNReal Compiled BanditRLProof/ScalarENNReal.lean:27
BanditRLProof.real_pseudoRegret_eq_univ_sum_model_gap_mul_natCast_pullCount theorem Foundations BanditRLProof.ScalarPseudoRegret Compiled BanditRLProof/ScalarPseudoRegret.lean:17
BanditRLProof.ENNReal.ofReal_pseudoRegret_eq_univ_sum_model_gap_ofReal_mul_natCast_pullCount_of_nonneg theorem Foundations BanditRLProof.ScalarPseudoRegret Compiled BanditRLProof/ScalarPseudoRegret.lean:41
BanditRLProof.Tsallis.halfTsallisPotentialProcess definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:24
BanditRLProof.Tsallis.sum_halfTsallisPotentialStability_eq_linearLoss_sum_add_terminal_sub_initial theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:35
BanditRLProof.Tsallis.importanceWeightedPotentialStabilityScore definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:94
BanditRLProof.Tsallis.refinedPotentialStabilityBound definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:107
BanditRLProof.Tsallis.measurable_linearLoss_of_coordinatewise theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:116
BanditRLProof.Tsallis.measurable_halfTsallisPotentialValue theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:131
BanditRLProof.Tsallis.measurable_importanceWeightedPotentialStabilityScore theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:171
BanditRLProof.Tsallis.measurable_refinedPotentialStabilityBound theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:245
BanditRLProof.Tsallis.halfTsallisPotentialStability_nonneg_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:259
BanditRLProof.Tsallis.integrable_refinedPotentialStabilityBound_of_finiteSimplex theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:308
BanditRLProof.Tsallis.integrable_importanceWeightedPotentialStabilityScore_finiteActionKernel theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:361
BanditRLProof.Tsallis.integrable_score_comp_history_action_of_condDistrib_generic theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:494
BanditRLProof.Tsallis.integral_importanceWeightedPotentialStabilityScore_le_integral_refinedBound_of_condDistrib_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:521
BanditRLProof.Tsallis.integral_sum_importanceWeightedPotentialStabilityScore_le_integral_sum_refinedBound_of_condDistrib_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:619
BanditRLProof.Tsallis.sampledHalfTsallisHistoryActionPotentialStabilityAt definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:739
BanditRLProof.Tsallis.sampledHalfTsallisRefinedPotentialStabilityBoundAt definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:752
BanditRLProof.Tsallis.measurable_sampledHalfTsallisHistoryActionPotentialStabilityAt theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:760
BanditRLProof.Tsallis.integrable_sampledHalfTsallisRefinedPotentialStabilityBoundAt theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:787
BanditRLProof.Tsallis.integrable_sampledHalfTsallisHistoryActionPotentialStabilityAt theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:814
BanditRLProof.Tsallis.sampledHalfTsallisSuccessorPotentialStabilityAt definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:870
BanditRLProof.Tsallis.integral_sum_sampledHalfTsallisSuccessorPotentialStability_le_integral_sum_refinedPotentialStabilityBound_canonical theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialFiniteHorizon Compiled BanditRLProof/TsallisConjugatePotentialFiniteHorizon.lean:894
BanditRLProof.Tsallis.halfTsallisPotentialValue definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:35
BanditRLProof.Tsallis.halfTsallisPotentialStability definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:49
BanditRLProof.Tsallis.halfTsallisConjugateCoordinateIncrement definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:62
BanditRLProof.Tsallis.halfTsallisConjugatePotentialUpper definition Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:70
BanditRLProof.Tsallis.one_add_eta_mul_shift_mul_sqrt_pos theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:78
BanditRLProof.Tsallis.halfTsallisConjugateCoordinateIncrement_eq theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:87
BanditRLProof.Tsallis.halfTsallisConjugateCoordinateIncrement_le theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:126
BanditRLProof.Tsallis.halfTsallis_fenchelCoordinate_le theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:184
BanditRLProof.Tsallis.halfTsallisConjugatePotentialUpper_le_shiftedMoments theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:224
BanditRLProof.Tsallis.importanceWeightedLoss_sub_selectedLoss_conjugate_domain theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:275
BanditRLProof.Tsallis.linearLoss_sub_linearLoss_eq_sum_sub_mul theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:329
BanditRLProof.Tsallis.sum_sub_mul_sub_baseline_eq_sum_sub_mul theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:340
BanditRLProof.Tsallis.linearLoss_sub_linearLoss_score_eq_sum_div_sqrt_of_stationary theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:360
BanditRLProof.Tsallis.halfTsallisPotentialStability_le_conjugatePotentialUpper_of_feasible theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:426
BanditRLProof.Tsallis.halfTsallisPotentialStability_importanceWeightedLoss_le_shiftedMoments_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:539
BanditRLProof.Tsallis.sum_prob_mul_halfTsallisPotentialStability_importanceWeightedLoss_le_refined_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:603
BanditRLProof.Tsallis.sum_halfTsallisMinimizer_mul_potentialStability_le_refined theorem Tsallis-FTRL BanditRLProof.TsallisConjugatePotentialStability Compiled BanditRLProof/TsallisConjugatePotentialStability.lean:692
BanditRLProof.Tsallis.linear_sub_quadratic_le_sq_div_four theorem Tsallis-FTRL BanditRLProof.TsallisConstrainedQuadraticOptimization Compiled BanditRLProof/TsallisConstrainedQuadraticOptimization.lean:18
BanditRLProof.Tsallis.sum_linear_sub_quadratic_le_unconstrained theorem Tsallis-FTRL BanditRLProof.TsallisConstrainedQuadraticOptimization Compiled BanditRLProof/TsallisConstrainedQuadraticOptimization.lean:26
BanditRLProof.Tsallis.sum_linear_sub_quadratic_le_of_sum_le theorem Tsallis-FTRL BanditRLProof.TsallisConstrainedQuadraticOptimization Compiled BanditRLProof/TsallisConstrainedQuadraticOptimization.lean:47
BanditRLProof.Tsallis.sum_inv_pos_of_nonempty theorem Tsallis-FTRL BanditRLProof.TsallisConstrainedQuadraticOptimization Compiled BanditRLProof/TsallisConstrainedQuadraticOptimization.lean:88
BanditRLProof.Tsallis.sum_erase_sqrt_le_sqrt_card theorem Tsallis-FTRL BanditRLProof.TsallisConstrainedQuadraticOptimization Compiled BanditRLProof/TsallisConstrainedQuadraticOptimization.lean:100
BanditRLProof.Tsallis.sum_erase_sqrt_probability_sub_gap_le_unconstrained theorem Tsallis-FTRL BanditRLProof.TsallisConstrainedQuadraticOptimization Compiled BanditRLProof/TsallisConstrainedQuadraticOptimization.lean:154
BanditRLProof.Tsallis.sum_erase_sqrt_probability_sub_gap_le_of_threshold theorem Tsallis-FTRL BanditRLProof.TsallisConstrainedQuadraticOptimization Compiled BanditRLProof/TsallisConstrainedQuadraticOptimization.lean:190
BanditRLProof.Tsallis.sampledScheduledHalfTsallisExpectedProbability_sum_le_unconstrained theorem Tsallis-FTRL BanditRLProof.TsallisConstrainedQuadraticOptimization Compiled BanditRLProof/TsallisConstrainedQuadraticOptimization.lean:251
BanditRLProof.Tsallis.sampledScheduledHalfTsallisExpectedProbability_sum_le_of_threshold theorem Tsallis-FTRL BanditRLProof.TsallisConstrainedQuadraticOptimization Compiled BanditRLProof/TsallisConstrainedQuadraticOptimization.lean:282
BanditRLProof.Tsallis.importanceWeightedStabilityScore definition Tsallis-FTRL BanditRLProof.TsallisFTRLConditionalStability Compiled BanditRLProof/TsallisFTRLConditionalStability.lean:25
BanditRLProof.Tsallis.halfPowerStabilityBound definition Tsallis-FTRL BanditRLProof.TsallisFTRLConditionalStability Compiled BanditRLProof/TsallisFTRLConditionalStability.lean:40
BanditRLProof.Tsallis.integral_importanceWeightedStabilityScore_le_integral_halfPowerStabilityBound_of_condDistrib_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisFTRLConditionalStability Compiled BanditRLProof/TsallisFTRLConditionalStability.lean:54
BanditRLProof.Tsallis.actionProcess_integral_importanceWeightedStabilityScore_le_integral_halfPowerStabilityBound_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisFTRLConditionalStability Compiled BanditRLProof/TsallisFTRLConditionalStability.lean:143
BanditRLProof.Tsallis.halfTsallisHistoryMinimizer definition Tsallis-FTRL BanditRLProof.TsallisFTRLConditionalStability Compiled BanditRLProof/TsallisFTRLConditionalStability.lean:198
BanditRLProof.Tsallis.halfTsallisHistoryUpdatedMinimizer definition Tsallis-FTRL BanditRLProof.TsallisFTRLConditionalStability Compiled BanditRLProof/TsallisFTRLConditionalStability.lean:207
BanditRLProof.Tsallis.measurableFiniteActionDistribution_halfTsallisHistoryMinimizer definition Tsallis-FTRL BanditRLProof.TsallisFTRLConditionalStability Compiled BanditRLProof/TsallisFTRLConditionalStability.lean:219
BanditRLProof.Tsallis.actionProcess_integral_halfTsallisHistoryStability_le_integral_halfPowerStabilityBound theorem Tsallis-FTRL BanditRLProof.TsallisFTRLConditionalStability Compiled BanditRLProof/TsallisFTRLConditionalStability.lean:245
BanditRLProof.Tsallis.sampledHalfTsallisProbabilityAtTime definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:20
BanditRLProof.Tsallis.sampledHalfTsallisObservedEstimatedLossAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:30
BanditRLProof.Tsallis.cumulativeLoss_sampledHalfTsallisObservedEstimatedLossAt_succ theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:41
BanditRLProof.Tsallis.halfTsallisCumulativeMinimizer_observedEstimatedLoss_eq_probabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:69
BanditRLProof.Tsallis.sampledHalfTsallisInitialStability definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:86
BanditRLProof.Tsallis.sampledHalfTsallisObservedSuccessorStabilityAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:100
BanditRLProof.Tsallis.sampledHalfTsallisInitialUpdatedAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:114
BanditRLProof.Tsallis.sampledHalfTsallisInitialHistoryActionStability definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:124
BanditRLProof.Tsallis.sum_observedEstimated_stability_eq_initial_add_successor theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:136
BanditRLProof.Tsallis.sampledHalfTsallis_observedEstimatedRegret_le theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:166
BanditRLProof.Tsallis.sampledHalfTsallisPredictableEstimatedLossAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:202
BanditRLProof.Tsallis.sampledHalfTsallisObservedEstimatedRegret definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:215
BanditRLProof.Tsallis.sampledHalfTsallisPredictableEnvironmentRegret definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:231
BanditRLProof.Tsallis.sampledHalfTsallisPredictableEstimatedRegret definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:246
BanditRLProof.Tsallis.measurable_sampledHalfTsallisProbabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:262
BanditRLProof.Tsallis.measurable_sampledHalfTsallisObservedEstimatedLossAt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:287
BanditRLProof.Tsallis.measurable_sampledHalfTsallisPredictableEstimatedLossAt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:306
BanditRLProof.Tsallis.sampledHalfTsallisObservedEstimatedLossAt_eq_predictable_ae theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:329
BanditRLProof.Tsallis.measurable_sampledHalfTsallisInitialUpdatedAt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:376
BanditRLProof.Tsallis.measurable_sampledHalfTsallisInitialHistoryActionStability theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:411
BanditRLProof.Tsallis.sampledHalfTsallisInitialStability_eq_historyAction_ae theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:433
BanditRLProof.Tsallis.sampledHalfTsallisObservedSuccessorStabilityAt_eq_predictable_ae theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:482
BanditRLProof.Tsallis.measurable_mixedImportanceWeightedLoss_of_coordinates theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:509
BanditRLProof.Tsallis.measurable_weightedImportanceWeightedLoss_of_coordinates theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:536
BanditRLProof.Tsallis.integrable_mixedImportanceWeightedLoss_finiteActionKernel theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:567
BanditRLProof.Tsallis.integrable_weightedImportanceWeightedLoss_finiteActionKernel theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:658
BanditRLProof.Tsallis.initialHalfTsallisEnvironmentDistributionSource definition Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:749
BanditRLProof.Tsallis.integrable_score_comp_history_action_of_condDistrib theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:763
BanditRLProof.Tsallis.integrable_mixed_weightedImportanceWeightedLoss_of_condDistrib theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:786
BanditRLProof.Tsallis.integral_mixed_weightedImportanceWeightedLoss_eq_predictable theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:833
BanditRLProof.Tsallis.sampledHalfTsallisPredictableEstimatedLossAt_first_moments theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:937
BanditRLProof.Tsallis.finiteSimplex_sampledHalfTsallisProbabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:1105
BanditRLProof.Tsallis.integrable_sampledHalfTsallisPredictableLinearLossAt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:1125
BanditRLProof.Tsallis.integral_sampledHalfTsallisPredictableEstimatedRegret_eq_environmentRegret theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:1211
BanditRLProof.Tsallis.sampledHalfTsallisObservedEstimatedRegret_eq_predictable_ae theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:1303
BanditRLProof.Tsallis.integral_sampledHalfTsallisObservedEstimatedRegret_eq_environmentRegret theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:1343
BanditRLProof.Tsallis.integral_sampledHalfTsallisInitialStability_le_halfPower theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:1387
BanditRLProof.Tsallis.integrable_sampledHalfTsallisSuccessorStabilitiesAt_canonical theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:1529
BanditRLProof.Tsallis.integral_sampledHalfTsallisPredictableEnvironmentRegret_le theorem Tsallis-FTRL BanditRLProof.TsallisFTRLEstimatedEnvironmentRegret Compiled BanditRLProof/TsallisFTRLEstimatedEnvironmentRegret.lean:1625
BanditRLProof.Tsallis.integrable_importanceWeightedStabilityScore_comp_history_action_of_condDistrib theorem Tsallis-FTRL BanditRLProof.TsallisFTRLExpectedStability Compiled BanditRLProof/TsallisFTRLExpectedStability.lean:29
BanditRLProof.Tsallis.integrable_halfPowerStabilityBound_comp_history theorem Tsallis-FTRL BanditRLProof.TsallisFTRLExpectedStability Compiled BanditRLProof/TsallisFTRLExpectedStability.lean:61
BanditRLProof.Tsallis.integral_sum_importanceWeightedStabilityScore_le_integral_sum_halfPowerStabilityBound_of_condDistrib_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisFTRLExpectedStability Compiled BanditRLProof/TsallisFTRLExpectedStability.lean:80
BanditRLProof.Tsallis.integral_sum_halfTsallisHistoryStability_le_integral_sum_halfPowerStabilityBound theorem Tsallis-FTRL BanditRLProof.TsallisFTRLExpectedStability Compiled BanditRLProof/TsallisFTRLExpectedStability.lean:190
BanditRLProof.Tsallis.halfTsallisSuccessorStabilityScore definition Tsallis-FTRL BanditRLProof.TsallisFTRLExpectedStability Compiled BanditRLProof/TsallisFTRLExpectedStability.lean:254
BanditRLProof.Tsallis.integral_sum_halfTsallisSuccessorStability_le_integral_sum_halfPowerStabilityBound_of_score_succ theorem Tsallis-FTRL BanditRLProof.TsallisFTRLExpectedStability Compiled BanditRLProof/TsallisFTRLExpectedStability.lean:279
BanditRLProof.Tsallis.halfTsallisCumulativeMinimizer definition Tsallis-FTRL BanditRLProof.TsallisFTRLFiniteHorizonSelection Compiled BanditRLProof/TsallisFTRLFiniteHorizonSelection.lean:22
BanditRLProof.Tsallis.halfTsallisCumulativeMinimizer_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisFTRLFiniteHorizonSelection Compiled BanditRLProof/TsallisFTRLFiniteHorizonSelection.lean:30
BanditRLProof.Tsallis.halfTsallisCumulativeMinimizer_succ theorem Tsallis-FTRL BanditRLProof.TsallisFTRLFiniteHorizonSelection Compiled BanditRLProof/TsallisFTRLFiniteHorizonSelection.lean:43
BanditRLProof.Tsallis.halfTsallisCumulativeMinimizer_succ_eq_updated theorem Tsallis-FTRL BanditRLProof.TsallisFTRLFiniteHorizonSelection Compiled BanditRLProof/TsallisFTRLFiniteHorizonSelection.lean:55
BanditRLProof.Tsallis.cumulativeLinearLoss_sub_comparator_le_stability_add_powerSumPenalty_half_canonical theorem Tsallis-FTRL BanditRLProof.TsallisFTRLFiniteHorizonSelection Compiled BanditRLProof/TsallisFTRLFiniteHorizonSelection.lean:73
BanditRLProof.Tsallis.HalfTsallisGeneratedSelectorMeasurability structure Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedMeasurability Compiled BanditRLProof/TsallisFTRLGeneratedMeasurability.lean:25
BanditRLProof.Tsallis.canonicalHalfTsallisFiniteHistorySelectorMeasurability definition Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedMeasurability Compiled BanditRLProof/TsallisFTRLGeneratedMeasurability.lean:41
BanditRLProof.Tsallis.measurable_importanceWeightedStabilityScore theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedMeasurability Compiled BanditRLProof/TsallisFTRLGeneratedMeasurability.lean:52
BanditRLProof.Tsallis.measurable_sampledHalfTsallisPredictableLossAt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedMeasurability Compiled BanditRLProof/TsallisFTRLGeneratedMeasurability.lean:96
BanditRLProof.Tsallis.measurable_sampledHalfTsallisUpdatedAt_canonical theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedMeasurability Compiled BanditRLProof/TsallisFTRLGeneratedMeasurability.lean:110
BanditRLProof.Tsallis.canonicalHalfTsallisGeneratedSelectorMeasurability definition Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedMeasurability Compiled BanditRLProof/TsallisFTRLGeneratedMeasurability.lean:186
BanditRLProof.Tsallis.measurable_sampledHalfTsallisHistoryActionStabilityAt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedMeasurability Compiled BanditRLProof/TsallisFTRLGeneratedMeasurability.lean:200
BanditRLProof.Tsallis.integral_sum_sampledHalfTsallisSuccessorStability_le_integral_sum_halfPowerStabilityBound_of_selector theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedMeasurability Compiled BanditRLProof/TsallisFTRLGeneratedMeasurability.lean:223
BanditRLProof.Tsallis.integral_sum_sampledHalfTsallisSuccessorStability_le_integral_sum_halfPowerStabilityBound_canonical theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedMeasurability Compiled BanditRLProof/TsallisFTRLGeneratedMeasurability.lean:250
BanditRLProof.Tsallis.finiteSimplex_apply_le_one theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedRegularity Compiled BanditRLProof/TsallisFTRLGeneratedRegularity.lean:20
BanditRLProof.Tsallis.prob_mul_abs_importanceWeightedStabilityScore_le theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedRegularity Compiled BanditRLProof/TsallisFTRLGeneratedRegularity.lean:31
BanditRLProof.Tsallis.integrable_finiteActionMeasure theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedRegularity Compiled BanditRLProof/TsallisFTRLGeneratedRegularity.lean:99
BanditRLProof.Tsallis.integrable_importanceWeightedStabilityScore_finiteActionKernel theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedRegularity Compiled BanditRLProof/TsallisFTRLGeneratedRegularity.lean:110
BanditRLProof.Tsallis.integrable_halfPowerStabilityBound_of_finiteSimplex theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedRegularity Compiled BanditRLProof/TsallisFTRLGeneratedRegularity.lean:195
BanditRLProof.Tsallis.sampledHalfTsallisPolicyAt_eq_finiteActionKernel theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedRegularity Compiled BanditRLProof/TsallisFTRLGeneratedRegularity.lean:238
BanditRLProof.Tsallis.integrable_sampledHalfTsallisHistoryActionStabilityAt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedRegularity Compiled BanditRLProof/TsallisFTRLGeneratedRegularity.lean:259
BanditRLProof.Tsallis.integrable_sampledHalfTsallisHalfPowerBoundAt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedRegularity Compiled BanditRLProof/TsallisFTRLGeneratedRegularity.lean:308
BanditRLProof.Tsallis.integral_sum_sampledHalfTsallisSuccessorStability_le_integral_sum_halfPowerStabilityBound_of_measurable theorem Tsallis-FTRL BanditRLProof.TsallisFTRLGeneratedRegularity Compiled BanditRLProof/TsallisFTRLGeneratedRegularity.lean:335
BanditRLProof.Tsallis.finiteSimplex_simplexPairShift_of_eq_zero_of_le theorem Tsallis-FTRL BanditRLProof.TsallisFTRLInteriority Compiled BanditRLProof/TsallisFTRLInteriority.lean:21
BanditRLProof.Tsallis.linearLoss_simplexPairShift_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLInteriority Compiled BanditRLProof/TsallisFTRLInteriority.lean:41
BanditRLProof.Tsallis.sum_sqrt_simplexPairShift_eq_of_eq_zero theorem Tsallis-FTRL BanditRLProof.TsallisFTRLInteriority Compiled BanditRLProof/TsallisFTRLInteriority.lean:55
BanditRLProof.Tsallis.sqrt_sub_sqrt_sub_le_div_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLInteriority Compiled BanditRLProof/TsallisFTRLInteriority.lean:90
BanditRLProof.Tsallis.exists_transfer_strictly_improves_half_objective theorem Tsallis-FTRL BanditRLProof.TsallisFTRLInteriority Compiled BanditRLProof/TsallisFTRLInteriority.lean:104
BanditRLProof.Tsallis.isRegularizedMinimizer_pos theorem Tsallis-FTRL BanditRLProof.TsallisFTRLInteriority Compiled BanditRLProof/TsallisFTRLInteriority.lean:168
BanditRLProof.Tsallis.exists_halfTsallisInteriorStationary_of_isRegularizedMinimizer_auto theorem Tsallis-FTRL BanditRLProof.TsallisFTRLInteriority Compiled BanditRLProof/TsallisFTRLInteriority.lean:212
BanditRLProof.Tsallis.sum_prob_mul_linearLoss_sub_next_importanceWeightedLoss_le_powerSum_half_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisFTRLInteriority Compiled BanditRLProof/TsallisFTRLInteriority.lean:227
BanditRLProof.Tsallis.extendFiniteWeights definition Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:20
BanditRLProof.Tsallis.extendFiniteWeights_apply_of_mem theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:25
BanditRLProof.Tsallis.extendFiniteWeights_apply_of_not_mem theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:33
BanditRLProof.Tsallis.sum_extendFiniteWeights theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:40
BanditRLProof.Tsallis.finiteSimplex_extendFiniteWeights theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:47
BanditRLProof.Tsallis.restrict_mem_stdSimplex_of_finiteSimplex theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:58
BanditRLProof.Tsallis.linearLoss_extendFiniteWeights_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:70
BanditRLProof.Tsallis.linearLoss_restrict_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:79
BanditRLProof.Tsallis.sum_sqrt_extendFiniteWeights_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:89
BanditRLProof.Tsallis.sum_sqrt_restrict_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:97
BanditRLProof.Tsallis.regularizedObjective_half_extendFiniteWeights_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:106
BanditRLProof.Tsallis.regularizedObjective_half_restrict_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:120
BanditRLProof.Tsallis.continuous_regularizedObjective_half_univ theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:135
BanditRLProof.Tsallis.exists_isRegularizedMinimizer_half theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:147
BanditRLProof.Tsallis.halfTsallisMinimizer definition Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:181
BanditRLProof.Tsallis.halfTsallisMinimizer_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:187
BanditRLProof.Tsallis.halfTsallisUpdatedMinimizer definition Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:197
BanditRLProof.Tsallis.halfTsallisUpdatedMinimizer_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:206
BanditRLProof.Tsallis.sum_halfTsallisMinimizer_mul_linearLoss_sub_updated_le_powerSum_half theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:223
BanditRLProof.Tsallis.exists_halfTsallisInteriorStationary_minimizer theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerExistence Compiled BanditRLProof/TsallisFTRLMinimizerExistence.lean:255
BanditRLProof.Tsallis.restrictedHalfTsallisMinimizer definition Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerMeasurability Compiled BanditRLProof/TsallisFTRLMinimizerMeasurability.lean:24
BanditRLProof.Tsallis.restrictedHalfTsallisMinimizer_mem_stdSimplex theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerMeasurability Compiled BanditRLProof/TsallisFTRLMinimizerMeasurability.lean:31
BanditRLProof.Tsallis.restrictedHalfTsallisMinimizer_isMinOn theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerMeasurability Compiled BanditRLProof/TsallisFTRLMinimizerMeasurability.lean:41
BanditRLProof.Tsallis.continuous_regularizedObjective_half_restricted_joint theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerMeasurability Compiled BanditRLProof/TsallisFTRLMinimizerMeasurability.lean:67
BanditRLProof.Tsallis.continuous_restrictedHalfTsallisMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerMeasurability Compiled BanditRLProof/TsallisFTRLMinimizerMeasurability.lean:80
BanditRLProof.Tsallis.halfTsallisMinimizer_eq_on_arms_of_score_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerMeasurability Compiled BanditRLProof/TsallisFTRLMinimizerMeasurability.lean:140
BanditRLProof.Tsallis.restrictedHalfTsallisMinimizer_restrict_score_apply theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerMeasurability Compiled BanditRLProof/TsallisFTRLMinimizerMeasurability.lean:175
BanditRLProof.Tsallis.measurable_halfTsallisMinimizer_comp theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerMeasurability Compiled BanditRLProof/TsallisFTRLMinimizerMeasurability.lean:191
BanditRLProof.Tsallis.strictConcaveOn_sum_sqrt_stdSimplex theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerUniqueness Compiled BanditRLProof/TsallisFTRLMinimizerUniqueness.lean:20
BanditRLProof.Tsallis.strictConvexOn_regularizedObjective_half_stdSimplex theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerUniqueness Compiled BanditRLProof/TsallisFTRLMinimizerUniqueness.lean:53
BanditRLProof.Tsallis.isRegularizedMinimizer_half_eq_on_arms theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerUniqueness Compiled BanditRLProof/TsallisFTRLMinimizerUniqueness.lean:96
BanditRLProof.Tsallis.halfTsallisMinimizer_eq_on_arms theorem Tsallis-FTRL BanditRLProof.TsallisFTRLMinimizerUniqueness Compiled BanditRLProof/TsallisFTRLMinimizerUniqueness.lean:146
BanditRLProof.Tsallis.HalfTsallisInteriorStationary definition Tsallis-FTRL BanditRLProof.TsallisFTRLOneStepStability Compiled BanditRLProof/TsallisFTRLOneStepStability.lean:41
BanditRLProof.Tsallis.halfTsallisInteriorStationary_rpow_sub_rpow_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLOneStepStability Compiled BanditRLProof/TsallisFTRLOneStepStability.lean:48
BanditRLProof.Tsallis.sub_le_two_mul_rpow_three_halves_mul_neg_half_rpow_sub theorem Tsallis-FTRL BanditRLProof.TsallisFTRLOneStepStability Compiled BanditRLProof/TsallisFTRLOneStepStability.lean:73
BanditRLProof.Tsallis.linearLoss_sub_next_importanceWeightedLoss_le theorem Tsallis-FTRL BanditRLProof.TsallisFTRLOneStepStability Compiled BanditRLProof/TsallisFTRLOneStepStability.lean:134
BanditRLProof.Tsallis.sum_prob_mul_linearLoss_sub_next_importanceWeightedLoss_le_powerSum_half theorem Tsallis-FTRL BanditRLProof.TsallisFTRLOneStepStability Compiled BanditRLProof/TsallisFTRLOneStepStability.lean:312
BanditRLProof.Tsallis.HalfTsallisFiniteHistorySelectorMeasurability structure Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:26
BanditRLProof.Tsallis.initialHalfTsallisDistribution definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:40
BanditRLProof.Tsallis.finiteActionDistribution_initialHalfTsallisDistribution theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:46
BanditRLProof.Tsallis.sampledHalfTsallisHistoryScore definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:61
BanditRLProof.Tsallis.sampledHalfTsallisHistoryScore_zero theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:80
BanditRLProof.Tsallis.sampledHalfTsallisHistoryScore_succ theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:92
BanditRLProof.Tsallis.measurable_sampledHalfTsallisHistoryScore theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:110
BanditRLProof.Tsallis.sampledHalfTsallisHistoryDistribution definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:189
BanditRLProof.Tsallis.sampledHalfTsallisHistoryDistributionSource definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:197
BanditRLProof.Tsallis.sampledHalfTsallisHistoryAlgorithm definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:218
BanditRLProof.Tsallis.sampledHalfTsallisHistoryAlgorithm_policy theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:242
BanditRLProof.Tsallis.sampledHalfTsallisTrajectoryKernel definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:257
BanditRLProof.Tsallis.sampledHalfTsallisTrajectoryMeasure_condDistrib_action theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:287
BanditRLProof.Tsallis.sampledHalfTsallisTrajectoryMeasure_condDistrib_action_given_environment theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:319
BanditRLProof.Tsallis.sampledHalfTsallisHistoryAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:363
BanditRLProof.Tsallis.sampledHalfTsallisActionAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:370
BanditRLProof.Tsallis.sampledHalfTsallisScoreAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:376
BanditRLProof.Tsallis.sampledHalfTsallisPredictableLossAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:383
BanditRLProof.Tsallis.sampledHalfTsallisProbabilityAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:391
BanditRLProof.Tsallis.sampledHalfTsallisUpdatedAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:399
BanditRLProof.Tsallis.sampledHalfTsallisHistoryActionStabilityAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:410
BanditRLProof.Tsallis.sampledHalfTsallisHalfPowerBoundAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:422
BanditRLProof.Tsallis.sampledHalfTsallisSuccessorStabilityAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:431
BanditRLProof.Tsallis.sampledHalfTsallisEnvironmentHistoryDistributionSource definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:449
BanditRLProof.Tsallis.sampledHalfTsallisPolicyAt definition Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:468
BanditRLProof.Tsallis.sampledHalfTsallisScoreAt_succ_ae theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:497
BanditRLProof.Tsallis.integral_sum_sampledHalfTsallisSuccessorStability_le_integral_sum_halfPowerStabilityBound theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRecursiveTrajectory Compiled BanditRLProof/TsallisFTRLRecursiveTrajectory.lean:550
BanditRLProof.FTRL.cumulativeLoss definition Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:23
BanditRLProof.FTRL.cumulativeLoss_zero theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:27
BanditRLProof.FTRL.cumulativeLoss_succ theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:34
BanditRLProof.FTRL.linearLoss_add_right theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:42
BanditRLProof.FTRL.linearLoss_cumulativeLoss theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:49
BanditRLProof.FTRL.regularizedObjective_cumulativeLoss_succ theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:58
BanditRLProof.FTRL.eta_mul_sum_next_linearLoss_add_regularizer_zero_le_objective theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:76
BanditRLProof.FTRL.sum_next_linearLoss_sub_comparator_le_regularizer_penalty theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:134
BanditRLProof.FTRL.cumulativeLinearLoss_sub_comparator_le_stability_add_penalty theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:181
BanditRLProof.FTRL.cumulativeLinearLoss_sub_comparator_le_stability_add_penalty_simplex theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:227
BanditRLProof.Tsallis.negEntropyRegularizer_sub_eq_powerSum_sub_div theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:254
BanditRLProof.Tsallis.cumulativeLinearLoss_sub_comparator_le_stability_add_powerSumPenalty theorem Tsallis-FTRL BanditRLProof.TsallisFTRLRegret Compiled BanditRLProof/TsallisFTRLRegret.lean:273
BanditRLProof.Tsallis.pairDirection definition Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:31
BanditRLProof.Tsallis.simplexPairShift definition Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:36
BanditRLProof.Tsallis.simplexPairShift_zero theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:41
BanditRLProof.Tsallis.sum_pairDirection_mul theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:47
BanditRLProof.Tsallis.sum_simplexPairShift theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:54
BanditRLProof.Tsallis.finiteSimplex_simplexPairShift_of_abs_lt_min theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:64
BanditRLProof.Tsallis.regularizedObjective_half_eq theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:87
BanditRLProof.Tsallis.hasDerivAt_simplexPairShift theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:98
BanditRLProof.Tsallis.hasDerivAt_linearLoss_simplexPairShift theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:107
BanditRLProof.Tsallis.sum_pairDirection_div_two_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:123
BanditRLProof.Tsallis.hasDerivAt_sum_sqrt_simplexPairShift theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:142
BanditRLProof.Tsallis.hasDerivAt_regularizedObjective_half_simplexPairShift theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:160
BanditRLProof.Tsallis.isLocalMin_regularizedObjective_half_simplexPairShift theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:192
BanditRLProof.Tsallis.halfTsallis_pairwise_stationary_of_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:220
BanditRLProof.Tsallis.exists_halfTsallisInteriorStationary_of_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:252
BanditRLProof.Tsallis.two_mul_sqrt_sub_sqrt_le_sub_div_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:272
BanditRLProof.Tsallis.isRegularizedMinimizer_of_halfTsallisInteriorStationary theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:287
BanditRLProof.Tsallis.isRegularizedMinimizer_iff_exists_halfTsallisInteriorStationary theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:361
BanditRLProof.Tsallis.sum_prob_mul_linearLoss_sub_next_importanceWeightedLoss_le_powerSum_half_of_positive_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisFTRLStationarity Compiled BanditRLProof/TsallisFTRLStationarity.lean:382
BanditRLProof.Tsallis.armDependentSuboptimalRewardBoostSource definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret.lean:11
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRewardCorruptionBudget_armDependentSuboptimalRewardBoostSource theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret.lean:33
BanditRLProof.Tsallis.finiteArmIIDArmDependentSuboptimalBoostRefinedRegime definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret.lean:65
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRefinedCorruptionWindow_armDependentSuboptimalRewardBoostSource_of_refinedRegime theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret.lean:85
BanditRLProof.Tsallis.finiteArmIIDArmDependentSuboptimalBoostAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret.lean:99
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDArmDependentSuboptimalBoostRewardLawRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDArmDependentSuboptimalBoostRegret.lean:123
BanditRLProof.Tsallis.clippedUnitReal definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:23
BanditRLProof.Tsallis.clippedUnitReal_mem_Icc theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:26
BanditRLProof.Tsallis.clippedUnitReal_eq_of_mem_Icc theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:30
BanditRLProof.Tsallis.abs_clippedUnitReal_add_sub_self_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:36
BanditRLProof.Tsallis.finiteArmIIDStationaryCorruptedReward definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:51
BanditRLProof.Tsallis.finiteArmIIDStationaryCorruptedRewardVectorLoss definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:56
BanditRLProof.Tsallis.measurable_finiteArmIIDStationaryCorruptedRewardVectorLoss theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:60
BanditRLProof.Tsallis.finiteArmIIDStationaryCorruptedRewardVectorLoss_nonneg theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:67
BanditRLProof.Tsallis.finiteArmIIDStationaryCorruptedRewardVectorLoss_le_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:77
BanditRLProof.Tsallis.abs_finiteArmIIDStationaryCorruptedReward_sub_base_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:86
BanditRLProof.Tsallis.abs_stationaryCorruptedLossDiff_sub_baseLossDiff_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:94
BanditRLProof.Tsallis.integrable_iidLossStateDiff theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:126
BanditRLProof.Tsallis.abs_iidLossStateMeanGap_stationaryCorrupted_sub_modelGap_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:149
BanditRLProof.Tsallis.scheduledGapDeviationBudget definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:205
BanditRLProof.Tsallis.scheduledGapDeviationBudget_eq theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:212
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_hasSelfBounding_of_perturbedExpectedGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:222
BanditRLProof.Tsallis.finiteArmIIDStationaryRewardCorruptionBudget definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:301
BanditRLProof.Tsallis.finiteArmIIDStationaryRewardCorruptionBudget_eq theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:307
BanditRLProof.Tsallis.finiteArmIIDStationaryRewardCorruptionBudget_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:317
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDStationaryCorruptedRewardLawRegret_le_log theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDCorruptedRewardLaw.lean:327
BanditRLProof.Tsallis.FiniteArmIIDHistoryAdaptiveRewardShiftSource structure Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:21
BanditRLProof.Tsallis.measurable_clippedUnitReal theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:35
BanditRLProof.Tsallis.measurable_finiteArmIIDHistoryAdaptiveCorruptedRewardLoss_initial theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:41
BanditRLProof.Tsallis.measurable_finiteArmIIDHistoryAdaptiveCorruptedRewardLoss_successor theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:66
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveCorruptedRewardLoss definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:99
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveCorruptedRewardLoss_hasIIDStateCoordinateLocality theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:126
BanditRLProof.Tsallis.predictableLossAt_finiteArmIIDHistoryAdaptiveCorruptedRewardLoss_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:139
BanditRLProof.Tsallis.predictableLossAt_finiteArmIIDHistoryAdaptiveCorruptedRewardLoss_succ theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:150
BanditRLProof.Tsallis.abs_historyAdaptiveCorruptedPredictableLossDiff_sub_baseLossDiff_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:163
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRewardCorruptionBudget definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:217
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRewardCorruptionBudget_eq theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:224
BanditRLProof.Tsallis.zeroFiniteArmIIDHistoryAdaptiveRewardShiftSource definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:235
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRewardCorruptionBudget_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:246
BanditRLProof.Tsallis.hasScheduledIIDPrefixKernelFactorization_sampledScheduledHalfTsallisFiniteArmIIDHistoryAdaptiveTrajectoryKernel theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:256
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLawRegret_le_log theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw.lean:278
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRewardShiftAt definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:12
BanditRLProof.Tsallis.measurable_finiteArmIIDHistoryAdaptiveRewardShiftAt theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:21
BanditRLProof.Tsallis.abs_finiteArmIIDHistoryAdaptiveRewardShiftAt_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:38
BanditRLProof.Tsallis.abs_historyAdaptiveCorruptedPredictableLossDiff_sub_baseLossDiff_le_actualShift theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:52
BanditRLProof.Tsallis.integrable_sampledScheduledHalfTsallisProbability_mul_historyAdaptiveRewardShiftDeviation theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:95
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveExpectedRewardCorruptionBudget definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:158
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveExpectedRewardCorruptionBudget_eq theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:175
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveExpectedRewardCorruptionBudget_nonneg theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:196
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveExpectedRewardCorruptionBudget_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:219
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw_hasSelfBounding theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:287
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLawRegret_le_log theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:418
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveExpectedRewardCorruptionBudgetForLaw definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:517
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveExpectedRefinedCorruptionWindow definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:538
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLawRegret_le_refinedLocalExplicit_of_window theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:553
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveExpectedCorruptionAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:686
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveExpectedCorruptionAllRegimeBound_fin_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:714
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLawRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:729
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostExpectedCorruptionRewardLawRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveExpectedCorruptedRewardLaw.lean:792
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLaw_hasSelfBounding theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveRefinedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveRefinedCorruptedRewardLaw.lean:13
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLawRegret_le_refinedLocalExplicit theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveRefinedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveRefinedCorruptedRewardLaw.lean:136
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRefinedCorruptionWindow definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveRefinedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveRefinedCorruptedRewardLaw.lean:251
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDHistoryAdaptiveCorruptedRewardLawRegret_le_refinedLocalExplicit_of_window theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHistoryAdaptiveRefinedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHistoryAdaptiveRefinedCorruptedRewardLaw.lean:264
BanditRLProof.Tsallis.FiniteArmIIDHorizonHistoryAdaptiveRewardShiftSource structure Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:20
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveRewardShiftSuccessor definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:37
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveRewardShiftEnvelope definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:47
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveRewardShiftSuccessor_of_lt theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:58
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveRewardShiftSuccessor_of_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:69
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveRewardShiftEnvelope_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:80
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveRewardShiftEnvelope_succ_of_lt theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:89
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveRewardShiftEnvelope_succ_of_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:101
BanditRLProof.Tsallis.FiniteArmIIDHorizonHistoryAdaptiveRewardShiftSource.toAllTime definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:115
BanditRLProof.Tsallis.FiniteArmIIDHorizonHistoryAdaptiveRewardShiftSource.toAllTime_initial theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:163
BanditRLProof.Tsallis.FiniteArmIIDHorizonHistoryAdaptiveRewardShiftSource.toAllTime_successor_of_lt theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:170
BanditRLProof.Tsallis.FiniteArmIIDHorizonHistoryAdaptiveRewardShiftSource.toAllTime_successor_of_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:181
BanditRLProof.Tsallis.FiniteArmIIDHorizonHistoryAdaptiveRewardShiftSource.toAllTime_envelope_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:191
BanditRLProof.Tsallis.FiniteArmIIDHorizonHistoryAdaptiveRewardShiftSource.toAllTime_envelope_succ_of_lt theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:199
BanditRLProof.Tsallis.FiniteArmIIDHorizonHistoryAdaptiveRewardShiftSource.toAllTime_envelope_succ_of_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:209
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveCorruptedRewardLoss definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:219
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveExpectedRewardCorruptionBudgetForLaw definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:226
BanditRLProof.Tsallis.finiteArmIIDHorizonHistoryAdaptiveExpectedCorruptionAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:235
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLawRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDHorizonHistoryAdaptiveExpectedCorruptedRewardLaw.lean:247
BanditRLProof.Tsallis.measurableHistoryArmGatedSuboptimalRewardBoostSource definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostRegret.lean:12
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRewardCorruptionBudget_measurableHistoryArmGatedSuboptimalRewardBoostSource theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostRegret.lean:61
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRefinedCorruptionWindow_measurableHistoryArmGatedSuboptimalRewardBoostSource_of_refinedRegime theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostRegret.lean:84
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostRewardLawRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDMeasurableHistoryArmGatedSuboptimalBoostRegret.lean:105
BanditRLProof.Tsallis.previousActionGatedSuboptimalRewardBoostSource definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDPreviousActionGatedSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDPreviousActionGatedSuboptimalBoostRegret.lean:12
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRewardCorruptionBudget_previousActionGatedSuboptimalRewardBoostSource theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDPreviousActionGatedSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDPreviousActionGatedSuboptimalBoostRegret.lean:62
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRefinedCorruptionWindow_previousActionGatedSuboptimalRewardBoostSource_of_refinedRegime theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDPreviousActionGatedSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDPreviousActionGatedSuboptimalBoostRegret.lean:81
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDPreviousActionGatedSuboptimalBoostRewardLawRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDPreviousActionGatedSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDPreviousActionGatedSuboptimalBoostRegret.lean:97
BanditRLProof.Tsallis.clippedUnitReward definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:20
BanditRLProof.Tsallis.clippedUnitReward_nonneg theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:23
BanditRLProof.Tsallis.clippedUnitReward_le_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:27
BanditRLProof.Tsallis.clippedUnitReward_eq_of_mem_Icc theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:31
BanditRLProof.Tsallis.measurable_clippedUnitReward theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:36
BanditRLProof.Tsallis.finiteArmIIDRewardVectorLaw definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:40
BanditRLProof.Tsallis.finiteArmIIDRewardVectorLoss definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:45
BanditRLProof.Tsallis.measurable_finiteArmIIDRewardVectorLoss theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:49
BanditRLProof.Tsallis.finiteArmIIDRewardVectorLoss_nonneg theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:54
BanditRLProof.Tsallis.finiteArmIIDRewardVectorLoss_le_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:60
BanditRLProof.Tsallis.integrable_clippedUnitReward theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:66
BanditRLProof.Tsallis.integral_finiteArmIIDRewardVectorLaw_clippedUnitReward_eq_mean theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:76
BanditRLProof.Tsallis.iidLossStateMeanGap_finiteArmIIDRewardVectorLoss_eq_gap theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:104
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDRewardLawRegret_le_log theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDRewardLaw.lean:160
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingCorruptedReward definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:19
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingCorruptedRewardVectorLoss definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:25
BanditRLProof.Tsallis.measurable_finiteArmIIDTimeVaryingCorruptedRewardVectorLoss theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:30
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingCorruptedRewardVectorLoss_nonneg theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:41
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingCorruptedRewardVectorLoss_le_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:52
BanditRLProof.Tsallis.abs_iidLossStateTimeVaryingMeanGap_corrupted_sub_modelGap_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:65
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingRewardCorruptionBudget definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:89
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingRewardCorruptionBudget_eq theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:96
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingRewardCorruptionBudget_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:107
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingRewardCorruptionBudget_const_eq_stationary theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:115
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDTimeVaryingCorruptedRewardLawRegret_le_log theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingCorruptedRewardLaw.lean:130
BanditRLProof.Tsallis.timeVaryingSuboptimalRewardBoostSource definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret.lean:11
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingSuboptimalBoostBudget definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret.lean:35
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRewardCorruptionBudget_timeVaryingSuboptimalRewardBoostSource theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret.lean:42
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingSuboptimalBoostRefinedRegime definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret.lean:59
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRefinedCorruptionWindow_timeVaryingSuboptimalRewardBoostSource_of_refinedRegime theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret.lean:79
BanditRLProof.Tsallis.finiteArmIIDTimeVaryingSuboptimalBoostAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret.lean:93
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDTimeVaryingSuboptimalBoostRewardLawRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret Compiled BanditRLProof/TsallisFiniteArmIIDTimeVaryingSuboptimalBoostRegret.lean:117
BanditRLProof.Tsallis.uniformSuboptimalRewardBoostSource definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret.lean:11
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRewardCorruptionBudget_uniformSuboptimalRewardBoostSource theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret.lean:31
BanditRLProof.Tsallis.finiteArmIIDUniformSuboptimalBoostRefinedRegime definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret.lean:73
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRefinedCorruptionWindow_uniformSuboptimalRewardBoostSource theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret.lean:91
BanditRLProof.Tsallis.finiteArmIIDHistoryAdaptiveRefinedCorruptionWindow_uniformSuboptimalRewardBoostSource_of_refinedRegime theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret.lean:149
BanditRLProof.Tsallis.finiteArmIIDUniformSuboptimalBoostAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret.lean:164
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDUniformSuboptimalBoostRewardLawRegret_le_refinedLocalExplicit theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret.lean:186
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIIDUniformSuboptimalBoostRewardLawRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIIDUniformSuboptimalBoostRefinedRegret.lean:275
BanditRLProof.Tsallis.finiteArmIndependentDriftingMeanAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanAllRegimes Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanAllRegimes.lean:21
BanditRLProof.Tsallis.finiteArmIndependentDriftingMeanAllRegimeBound_fin_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanAllRegimes Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanAllRegimes.lean:46
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentDriftingMeanRewardLawRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanAllRegimes Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanAllRegimes.lean:61
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableMovingComparatorEnvironmentRegret definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:25
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableMovingComparatorEnvironmentRegret_eq_fixed_add theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:41
BanditRLProof.Tsallis.finiteArmIndependentBestArmAt definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:66
BanditRLProof.Tsallis.finiteArmIndependentRewardMean_le_bestArmAt theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:75
BanditRLProof.Tsallis.finiteArmIndependentDynamicComparatorPenalty definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:90
BanditRLProof.Tsallis.finiteArmIndependentDynamicComparatorPenalty_fin_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:104
BanditRLProof.Tsallis.finiteArmIndependentRewardMean_sub_bestArm_le_meanDeviation theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:117
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentMovingComparatorRewardLawRegret_eq_fixed_add_meanAdvantage theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:155
BanditRLProof.Tsallis.finiteArmIndependentDriftingMeanDynamicAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:308
BanditRLProof.Tsallis.finiteArmIndependentDriftingMeanDynamicAllRegimeBound_fin_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:318
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentDriftingMeanDynamicRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanDynamicRegret.lean:330
BanditRLProof.Tsallis.finiteArmIndependentDriftingMeanRefinedCorruptionWindow definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRefinedRegret.lean:22
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentDriftingMeanRewardLawRegret_le_refinedLocalExplicit_of_window theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRefinedRegret Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRefinedRegret.lean:35
BanditRLProof.Tsallis.finiteArmIndependentRewardMean definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRewardLaw.lean:18
BanditRLProof.Tsallis.independentLossStateTimeVaryingMeanGap_finiteArmIndependentRewardVectorLoss_eq_mean_sub theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRewardLaw.lean:24
BanditRLProof.Tsallis.abs_independentLossStateTimeVaryingMeanGap_sub_modelGap_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRewardLaw.lean:81
BanditRLProof.Tsallis.finiteArmIndependentMeanDeviationBudget definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRewardLaw.lean:126
BanditRLProof.Tsallis.finiteArmIndependentMeanDeviationBudget_eq theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRewardLaw.lean:134
BanditRLProof.Tsallis.finiteArmIndependentMeanDeviationBudget_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRewardLaw.lean:145
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentDriftingMeanRewardLaw_hasSelfBounding theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRewardLaw.lean:155
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentDriftingMeanRewardLawRegret_le_log theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentDriftingMeanRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentDriftingMeanRewardLaw.lean:277
BanditRLProof.Tsallis.finiteArmIndependentCumulativeGlobalMeanSwitchCount_nonneg theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret.lean:19
BanditRLProof.Tsallis.finiteArmIndependentCumulativeGlobalMeanSwitchCount_mono theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret.lean:29
BanditRLProof.Tsallis.finiteArmIndependentMeanDeviationBudget_globalMeanSwitchCount_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret.lean:42
BanditRLProof.Tsallis.finiteArmIndependentDynamicComparatorPenalty_globalMeanSwitchCount_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret.lean:94
BanditRLProof.Tsallis.finiteArmIndependentGlobalMeanSwitchCount_totalBudget_le theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret.lean:165
BanditRLProof.Tsallis.finiteArmIndependentGlobalMeanSwitchCountHorizonCompressedLogDynamicBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret.lean:189
BanditRLProof.Tsallis.finiteArmIndependentGlobalMeanSwitchCountHorizonCompressedLogDynamicBound_fin_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret.lean:202
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentGlobalMeanSwitchCountHorizonCompressedDynamicRegret_le_log theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountCompressedDynamicRegret.lean:218
BanditRLProof.Tsallis.finiteArmIndependentCumulativeGlobalMeanSwitchCount definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret.lean:19
BanditRLProof.Tsallis.finiteArmIndependentCumulativeGlobalMeanSwitchCount_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret.lean:31
BanditRLProof.Tsallis.finiteArmIndependentCumulativeGlobalMeanSwitchCount_eq_card theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret.lean:38
BanditRLProof.Tsallis.finiteArmIndependentCumulativeMeanSwitchCount_le_globalMeanSwitchCount theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret.lean:49
BanditRLProof.Tsallis.finiteArmIndependentCumulativeMeanPathVariation_le_globalMeanSwitchCount theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret.lean:76
BanditRLProof.Tsallis.abs_finiteArmIndependentRewardMean_sub_model_le_globalMeanSwitchCount theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret.lean:92
BanditRLProof.Tsallis.finiteArmIndependentGlobalMeanSwitchCountDynamicAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret.lean:113
BanditRLProof.Tsallis.finiteArmIndependentGlobalMeanSwitchCountDynamicAllRegimeBound_fin_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret.lean:122
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentGlobalMeanSwitchCountDynamicRegret.lean:135
BanditRLProof.Tsallis.finiteArmIndependentRewardMean_mem_Icc theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret.lean:20
BanditRLProof.Tsallis.finiteArmIndependentCumulativeMeanSwitchCount definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret.lean:49
BanditRLProof.Tsallis.finiteArmIndependentCumulativeMeanSwitchCount_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret.lean:61
BanditRLProof.Tsallis.finiteArmIndependentCumulativeMeanSwitchCount_eq_card theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret.lean:68
BanditRLProof.Tsallis.finiteArmIndependentCumulativeMeanPathVariation_le_switchCount theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret.lean:81
BanditRLProof.Tsallis.abs_finiteArmIndependentRewardMean_sub_model_le_switchCount theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret.lean:110
BanditRLProof.Tsallis.finiteArmIndependentMeanSwitchCountDynamicAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret.lean:131
BanditRLProof.Tsallis.finiteArmIndependentMeanSwitchCountDynamicAllRegimeBound_fin_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret.lean:139
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentMeanSwitchCountDynamicRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentMeanSwitchCountDynamicRegret.lean:152
BanditRLProof.Tsallis.finiteArmIndependentCumulativeMeanPathVariation definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentPathVariationDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentPathVariationDynamicRegret.lean:20
BanditRLProof.Tsallis.finiteArmIndependentCumulativeMeanPathVariation_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentPathVariationDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentPathVariationDynamicRegret.lean:27
BanditRLProof.Tsallis.abs_finiteArmIndependentRewardMean_sub_zero_le_cumulativeMeanPathVariation theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentPathVariationDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentPathVariationDynamicRegret.lean:32
BanditRLProof.Tsallis.abs_finiteArmIndependentRewardMean_sub_model_le_cumulativeMeanPathVariation theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentPathVariationDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentPathVariationDynamicRegret.lean:72
BanditRLProof.Tsallis.finiteArmIndependentPathVariationDynamicAllRegimeBound definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentPathVariationDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentPathVariationDynamicRegret.lean:91
BanditRLProof.Tsallis.finiteArmIndependentPathVariationDynamicAllRegimeBound_fin_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentPathVariationDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentPathVariationDynamicRegret.lean:99
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentPathVariationDynamicRegret_le_allRegimes theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentPathVariationDynamicRegret Compiled BanditRLProof/TsallisFiniteArmIndependentPathVariationDynamicRegret.lean:112
BanditRLProof.Tsallis.finiteArmIndependentRewardVectorLaw definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentRewardLaw.lean:20
BanditRLProof.Tsallis.independentLossStateTimeVaryingMeanGap_finiteArmIndependentRewardVectorLoss_eq_gap theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentRewardLaw.lean:27
BanditRLProof.Tsallis.hasScheduledIndependentMeanGapLaw_of_finiteArmIndependentRewardVectorLaw theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentRewardLaw.lean:49
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteArmIndependentRewardLawRegret_le_log theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentRewardLaw Compiled BanditRLProof/TsallisFiniteArmIndependentRewardLaw.lean:103
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionModel definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:20
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionModel_bestArm theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:25
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionLaw definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:32
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionLaw_isProbabilityMeasure theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:41
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionLaw_mem_Icc_ae theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:48
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionMean_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:58
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionMean_one_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:67
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionMean_one_succ theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:75
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionInitialMean theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:83
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionGap_pos theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:92
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionGap_le_one theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:106
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionBestArmAt_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:120
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionBestArmAt_succ theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:151
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionIndicator theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:183
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchObstructionGlobalCount_succ theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:219
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchComparatorAdvantage definition Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:230
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchComparatorAdvantage_zero theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:243
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchComparatorAdvantage_eq theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:250
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchDynamicComparatorPenalty_eq theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:267
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchComparatorAdvantage_gt_nat_mul_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:292
BanditRLProof.Tsallis.finiteArmIndependentSingleSwitchDynamicComparatorRouteObstruction theorem Tsallis-FTRL BanditRLProof.TsallisFiniteArmIndependentSingleSwitchComparatorObstruction Compiled BanditRLProof/TsallisFiniteArmIndependentSingleSwitchComparatorObstruction.lean:325
BanditRLProof.Exp3.finiteBanditMeanLoss definition Tsallis-FTRL BanditRLProof.TsallisFiniteBanditMeanLoss Compiled BanditRLProof/TsallisFiniteBanditMeanLoss.lean:26
BanditRLProof.Exp3.finiteBanditMeanLoss_initial theorem Tsallis-FTRL BanditRLProof.TsallisFiniteBanditMeanLoss Compiled BanditRLProof/TsallisFiniteBanditMeanLoss.lean:53
BanditRLProof.Exp3.finiteBanditMeanLoss_successor theorem Tsallis-FTRL BanditRLProof.TsallisFiniteBanditMeanLoss Compiled BanditRLProof/TsallisFiniteBanditMeanLoss.lean:64
BanditRLProof.Exp3.predictableLossAt_finiteBanditMeanLoss theorem Tsallis-FTRL BanditRLProof.TsallisFiniteBanditMeanLoss Compiled BanditRLProof/TsallisFiniteBanditMeanLoss.lean:77
BanditRLProof.Exp3.predictableLossAt_finiteBanditMeanLoss_sub_bestArm_eq_gap theorem Tsallis-FTRL BanditRLProof.TsallisFiniteBanditMeanLoss Compiled BanditRLProof/TsallisFiniteBanditMeanLoss.lean:90
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisFiniteBanditMeanLossRegret_le_log_fixedGap theorem Tsallis-FTRL BanditRLProof.TsallisFiniteBanditMeanLoss Compiled BanditRLProof/TsallisFiniteBanditMeanLoss.lean:115
BanditRLProof.Tsallis.powerWeightedSquaredImportanceWeightedLoss definition Tsallis-FTRL BanditRLProof.TsallisImportanceWeightedMoment Compiled BanditRLProof/TsallisImportanceWeightedMoment.lean:27
BanditRLProof.Tsallis.powerWeightedSquaredImportanceWeightedLoss_eq_selected theorem Tsallis-FTRL BanditRLProof.TsallisImportanceWeightedMoment Compiled BanditRLProof/TsallisImportanceWeightedMoment.lean:38
BanditRLProof.Tsallis.sum_prob_mul_powerWeightedSquaredImportanceWeightedLoss_eq theorem Tsallis-FTRL BanditRLProof.TsallisImportanceWeightedMoment Compiled BanditRLProof/TsallisImportanceWeightedMoment.lean:64
BanditRLProof.Tsallis.sum_prob_mul_powerWeightedSquaredImportanceWeightedLoss_le_powerSum theorem Tsallis-FTRL BanditRLProof.TsallisImportanceWeightedMoment Compiled BanditRLProof/TsallisImportanceWeightedMoment.lean:87
BanditRLProof.Tsallis.oracleRestartEpochRounds definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartDynamicRegret Compiled BanditRLProof/TsallisOracleRestartDynamicRegret.lean:21
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableOracleRestartEpochRegret definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartDynamicRegret Compiled BanditRLProof/TsallisOracleRestartDynamicRegret.lean:27
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableMovingComparatorEnvironmentRegret_eq_sum_oracleRestartEpochRegret theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartDynamicRegret Compiled BanditRLProof/TsallisOracleRestartDynamicRegret.lean:46
BanditRLProof.Tsallis.sum_sqrt_oracleRestartEpochRounds_card_le theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartDynamicRegret Compiled BanditRLProof/TsallisOracleRestartDynamicRegret.lean:75
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableMovingComparatorEnvironmentRegret_le_oracleRestartSqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartDynamicRegret Compiled BanditRLProof/TsallisOracleRestartDynamicRegret.lean:109
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableMovingComparatorEnvironmentRegret_le_oracleRestartSwitchCountSqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartDynamicRegret Compiled BanditRLProof/TsallisOracleRestartDynamicRegret.lean:162
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableEstimatedLossAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:21
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedEstimatedLossAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:36
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisProbabilityAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:48
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisEnvironmentHistoryDistributionSource definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:58
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPolicyAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:78
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPolicyAt_eq_finiteActionKernel theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:103
BanditRLProof.Tsallis.measurable_sampledOracleRestartHalfTsallisProbabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:123
BanditRLProof.Tsallis.measurable_sampledOracleRestartHalfTsallisPredictableEstimatedLossAt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:143
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedEstimatedLossAt_eq_predictable_ae theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:167
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableEstimatedLossAt_first_moments theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:217
BanditRLProof.Tsallis.finiteSimplex_sampledOracleRestartHalfTsallisProbabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:391
BanditRLProof.Tsallis.integrable_sampledOracleRestartHalfTsallisPredictableLinearLossAt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:420
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableScheduleEpochEstimatedRegret definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:518
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:538
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableScheduleEpochEnvironmentRegret definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:556
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisPredictableScheduleEpochEstimatedRegret_eq_environmentRegret theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:575
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret_eq_predictable_ae theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:677
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableScheduleEpochEnvironmentRegret_pointMass_eq theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:716
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisPredictableScheduleEpochEstimatedRegret_pointMass_eq_epochRegret theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:743
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret_pointMass_eq_epochRegret theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:794
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisPredictableScheduleEpochRegret_le_of_estimatedRegret_le theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:846
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_le_scheduleSqrt_of_epochEstimatedRegret theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:883
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_le_scheduleSwitchCountSqrt_of_epochEstimatedRegret theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:1029
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_le_scheduleSqrt_of_epochObservedEstimatedRegret theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:1099
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_le_scheduleSwitchCountSqrt_of_epochObservedEstimatedRegret theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedRegret Compiled BanditRLProof/TsallisOracleRestartExpectedRegret.lean:1170
BanditRLProof.Tsallis.oracleRestartLocalTime definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:21
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:26
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisActionAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:33
BanditRLProof.Tsallis.frestrictLe_oracleRestartShiftedTrajectory_eq_localPairHistory theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:40
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisScoreAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:52
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableLossAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:68
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisUpdatedAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:76
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryActionPotentialStabilityAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:97
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisRefinedPotentialStabilityBoundAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:115
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedPotentialStabilityAtSuccessor definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:128
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedPotentialStabilityAtSuccessor_eq_shifted theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:158
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisShiftedPotentialStabilityAtSuccessor_eq_historyAction_ae theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:238
BanditRLProof.Tsallis.measurable_sampledOracleRestartHalfTsallisScoreAt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:304
BanditRLProof.Tsallis.measurable_sampledOracleRestartHalfTsallisUpdatedAt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:333
BanditRLProof.Tsallis.measurable_sampledOracleRestartHalfTsallisHistoryActionPotentialStabilityAt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:404
BanditRLProof.Tsallis.integrable_sampledOracleRestartHalfTsallisRefinedPotentialStabilityBoundAt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:434
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisProbabilityAt_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:460
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisUpdatedAt_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:507
BanditRLProof.Tsallis.integrable_sampledOracleRestartHalfTsallisHistoryActionPotentialStabilityAt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:534
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisHistoryActionPotentialStabilityAt_le_one theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:585
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisShiftedPotentialStabilityAtSuccessor_le_one theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:696
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisShiftedPotentialStabilityAtSuccessor_le_refined theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:753
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisInitialPotentialStabilityAtTime_le_one theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:897
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisShiftedPotentialStabilityAtTime_le_integral_one theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:1073
BanditRLProof.Tsallis.integral_sum_sampledOracleRestartHalfTsallisShiftedPotentialStabilityAtLocalPrefix_le_card theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:1109
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret_pointMass_le_card_add_penalty_of_epochRounds_eq theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartExpectedStability Compiled BanditRLProof/TsallisOracleRestartExpectedStability.lean:1188
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_sqrtSchedule_le_scheduleSqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedDynamicRegret Compiled BanditRLProof/TsallisOracleRestartGeneratedDynamicRegret.lean:21
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_sqrtSchedule_le_scheduleSwitchCountSqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedDynamicRegret Compiled BanditRLProof/TsallisOracleRestartGeneratedDynamicRegret.lean:67
BanditRLProof.Tsallis.OracleRestartSchedule structure Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:20
BanditRLProof.Tsallis.oracleNeverRestartSchedule definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:27
BanditRLProof.Tsallis.oracleRestartEveryRoundSchedule definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:34
BanditRLProof.Tsallis.OracleRestartSchedule.start_succ_le_of_ne theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:42
BanditRLProof.Tsallis.oracleRestartLocalPairHistory definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:51
BanditRLProof.Tsallis.oracleRestartLocalPairHistory_zero theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:61
BanditRLProof.Tsallis.measurable_oracleRestartLocalPairHistory theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:69
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryDistribution definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:86
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryDistribution_of_boundary theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:102
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryDistribution_of_continuation theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:114
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryDistribution_pos theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:131
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryDistribution_neverRestart theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:166
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryDistribution_restartEveryRound theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:179
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryDistributionSource definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:190
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryAlgorithm definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:232
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisHistoryAlgorithm_policy theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:259
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisProbabilityAtTime definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:275
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisProbabilityAtTime_neverRestart theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:286
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisProbabilityAtTime_restartEveryRound theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:301
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisTrajectoryKernel definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:314
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisTrajectoryMeasure_condDistrib_action theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:343
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisTrajectoryMeasure_condDistrib_action_given_environment theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGeneratedTrajectory Compiled BanditRLProof/TsallisOracleRestartGeneratedTrajectory.lean:378
BanditRLProof.Tsallis.oracleChangePointRestartStart definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:21
BanditRLProof.Tsallis.oracleChangePointRestartSchedule definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:29
BanditRLProof.Tsallis.oracleChangePointRestartSchedule_start_zero theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:47
BanditRLProof.Tsallis.oracleChangePointRestartSchedule_start_succ theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:52
BanditRLProof.Tsallis.oracleRestartScheduleEpochs_oracleChangePointRestartSchedule theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:60
BanditRLProof.Tsallis.oracleRestartScheduleEpochs_card_oracleChangePointRestartSchedule theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:99
BanditRLProof.Tsallis.finiteArmIndependentGlobalMeanChangeAt definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:113
BanditRLProof.Tsallis.finiteArmIndependentGlobalMeanChangeTimes definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:120
BanditRLProof.Tsallis.finiteArmIndependentGlobalMeanChangeRestartSchedule definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:128
BanditRLProof.Tsallis.oracleRestartScheduleEpochs_card_finiteArmIndependentGlobalMeanChangeRestartSchedule theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:137
BanditRLProof.Tsallis.finiteArmIndependentCumulativeGlobalMeanSwitchCount_eq_changeTimes_card theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:153
BanditRLProof.Tsallis.oracleRestartScheduleEpochs_card_cast_finiteArmIndependentGlobalMeanChangeRestartSchedule theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:171
BanditRLProof.Tsallis.finiteArmIndependentRewardMean_eq_globalMeanChangeRestartStart theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:186
BanditRLProof.Tsallis.finiteArmIndependentRewardMean_le_globalMeanChangeRestartBestArm theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:218
BanditRLProof.Tsallis.independentLossStateTimeVaryingMeanGap_globalMeanChangeRestartBestArm_nonneg theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:243
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisFiniteArmIndependentGlobalMeanChangeDynamicRegret_le theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartGlobalMeanSwitchCount Compiled BanditRLProof/TsallisOracleRestartGlobalMeanSwitchCount.lean:272
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableEnvironmentRegret definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:22
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:39
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableEnvironmentRegret_neverRestart theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:55
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_neverRestart theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:70
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_eq_fixed_add theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:88
BanditRLProof.Tsallis.oracleRestartScheduleEpochs definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:115
BanditRLProof.Tsallis.oracleRestartSchedule_start_mem_epochs theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:119
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableScheduleEpochRegret definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:126
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_eq_sum_scheduleEpochRegret theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:144
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_le_scheduleSqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:175
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisPredictableMovingComparatorEnvironmentRegret_le_scheduleSwitchCountSqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartPredictableRegret Compiled BanditRLProof/TsallisOracleRestartPredictableRegret.lean:233
BanditRLProof.Tsallis.refinedPotentialStabilityBound_le_two_mul_eta_mul_sqrt_erase_card theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:25
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisShiftedPotentialStabilityAtSuccessor_le_two_mul_eta_mul_sqrt_erase_card theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:73
BanditRLProof.Tsallis.one_div_natSucc_le_one_div_sqrt_natSucc theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:155
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSqrtSchedule_two_mul theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:172
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSqrtSchedule_two_mul_sq theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:183
BanditRLProof.Tsallis.one_div_sampledScheduledHalfTsallisSqrtSchedule theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:190
BanditRLProof.Tsallis.sum_range_sampledScheduledHalfTsallisSqrtSchedule_refinedBudget_le_three_mul_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:203
BanditRLProof.Tsallis.integral_sum_sampledOracleRestartHalfTsallisShiftedPotentialStabilityAtLocalPrefix_sqrtSchedule_le_four_mul_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:277
BanditRLProof.Tsallis.initialHalfTsallisPotentialMass_sqrtSchedule_pointMassPenalty_le_four_mul_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:476
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret_pointMass_sqrtSchedule_le_eight_mul_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:558
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret_pointMass_sqrtSchedule_le_eight_mul_sqrt_card theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:683
BanditRLProof.Tsallis.integral_sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret_pointMass_sqrtSchedule_le_eight_mul_sqrt_card_of_mem theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartRefinedStabilityTuning Compiled BanditRLProof/TsallisOracleRestartRefinedStabilityTuning.lean:725
BanditRLProof.Tsallis.oracleRestartShiftedTrajectory definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:18
BanditRLProof.Tsallis.oracleRestartShiftedTrajectory_fst theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:25
BanditRLProof.Tsallis.oracleRestartShiftedTrajectory_snd_apply theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:32
BanditRLProof.Tsallis.OracleRestartSchedule.monotone_start theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:41
BanditRLProof.Tsallis.OracleRestartSchedule.start_start theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:54
BanditRLProof.Tsallis.OracleRestartSchedule.start_eq_of_between theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:65
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisProbabilityAtTime_eq_scheduled_shift theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:79
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedEstimatedLossAt_eq_scheduled_shift theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:126
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisProbabilityAtTime_add_eq_scheduled_of_start_eq theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:146
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedEstimatedLossAt_add_eq_scheduled_of_start_eq theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:163
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisLocalPrefixObservedEstimatedRegret definition Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:180
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisLocalPrefixObservedEstimatedRegret_eq_scheduled theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:199
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisLocalPrefixObservedEstimatedRegret_pointMass_le_stability_add_penalty theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:229
BanditRLProof.Tsallis.exists_oracleRestartEpochRounds_eq_image_range theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:266
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret_eq_localPrefix_of_epochRounds_eq theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:335
BanditRLProof.Tsallis.sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret_pointMass_le_stability_add_penalty_of_epochRounds_eq theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:358
BanditRLProof.Tsallis.exists_sampledOracleRestartHalfTsallisObservedScheduleEpochEstimatedRegret_pointMass_le_stability_add_penalty theorem Tsallis-FTRL BanditRLProof.TsallisOracleRestartScoreAlignment Compiled BanditRLProof/TsallisOracleRestartScoreAlignment.lean:412
BanditRLProof.Tsallis.CounterAction abbreviation Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:22
BanditRLProof.Tsallis.counterArms definition Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:24
BanditRLProof.Tsallis.counterEta definition Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:26
BanditRLProof.Tsallis.counterProb definition Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:28
BanditRLProof.Tsallis.counterScore definition Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:31
BanditRLProof.Tsallis.counterLoss definition Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:34
BanditRLProof.Tsallis.counterNext definition Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:38
BanditRLProof.Tsallis.counterNextMultiplier definition Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:47
BanditRLProof.Tsallis.sqrt_49 theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:51
BanditRLProof.Tsallis.sqrt_576 theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:54
BanditRLProof.Tsallis.sqrt_625 theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:57
BanditRLProof.Tsallis.sqrt_24778200568643041 theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:60
BanditRLProof.Tsallis.sqrt_1813828968643041 theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:65
BanditRLProof.Tsallis.sqrt_22964371600000000 theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:70
BanditRLProof.Tsallis.sqrt_1524122302720081 theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:75
BanditRLProof.Tsallis.sqrt_120121402720081 theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:80
BanditRLProof.Tsallis.sqrt_1404000900000000 theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:85
BanditRLProof.Tsallis.counterEta_pos theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:90
BanditRLProof.Tsallis.counterEta_le_one theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:93
BanditRLProof.Tsallis.counterProb_simplex theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:96
BanditRLProof.Tsallis.counterProb_pos theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:103
BanditRLProof.Tsallis.counterLoss_mem_Icc theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:108
BanditRLProof.Tsallis.counterNext_simplex theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:113
BanditRLProof.Tsallis.counterNext_pos theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:122
BanditRLProof.Tsallis.rpow_neg_half_eq_inv_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:128
BanditRLProof.Tsallis.counterProb_stationary theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:133
BanditRLProof.Tsallis.counterNext_stationary theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:142
BanditRLProof.Tsallis.counterProb_minimizer theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:159
BanditRLProof.Tsallis.counterNext_minimizer theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:167
BanditRLProof.Tsallis.exists_minimizer_counterexample_to_refinedAveragedStability theorem Tsallis-FTRL BanditRLProof.TsallisRefinedAveragedStabilityObstruction Compiled BanditRLProof/TsallisRefinedAveragedStabilityObstruction.lean:188
BanditRLProof.Tsallis.shiftedHalfPowerImportanceWeightedMoment definition Tsallis-FTRL BanditRLProof.TsallisRefinedImportanceWeightedMoment Compiled BanditRLProof/TsallisRefinedImportanceWeightedMoment.lean:27
BanditRLProof.Tsallis.shiftedPositiveCubicImportanceWeightedMoment definition Tsallis-FTRL BanditRLProof.TsallisRefinedImportanceWeightedMoment Compiled BanditRLProof/TsallisRefinedImportanceWeightedMoment.lean:36
BanditRLProof.Tsallis.sum_mul_sum_erase_eq_sum_mul_one_sub theorem Tsallis-FTRL BanditRLProof.TsallisRefinedImportanceWeightedMoment Compiled BanditRLProof/TsallisRefinedImportanceWeightedMoment.lean:46
BanditRLProof.Tsallis.prob_mul_shiftedHalfPowerImportanceWeightedMoment_eq theorem Tsallis-FTRL BanditRLProof.TsallisRefinedImportanceWeightedMoment Compiled BanditRLProof/TsallisRefinedImportanceWeightedMoment.lean:89
BanditRLProof.Tsallis.sum_prob_mul_shiftedHalfPowerImportanceWeightedMoment_le theorem Tsallis-FTRL BanditRLProof.TsallisRefinedImportanceWeightedMoment Compiled BanditRLProof/TsallisRefinedImportanceWeightedMoment.lean:136
BanditRLProof.Tsallis.prob_mul_shiftedPositiveCubicImportanceWeightedMoment_eq theorem Tsallis-FTRL BanditRLProof.TsallisRefinedImportanceWeightedMoment Compiled BanditRLProof/TsallisRefinedImportanceWeightedMoment.lean:195
BanditRLProof.Tsallis.sum_prob_mul_shiftedPositiveCubicImportanceWeightedMoment_le_one theorem Tsallis-FTRL BanditRLProof.TsallisRefinedImportanceWeightedMoment Compiled BanditRLProof/TsallisRefinedImportanceWeightedMoment.lean:226
BanditRLProof.Tsallis.sum_prob_mul_stability_le_refinedHalfPower_add_square theorem Tsallis-FTRL BanditRLProof.TsallisRefinedImportanceWeightedMoment Compiled BanditRLProof/TsallisRefinedImportanceWeightedMoment.lean:300
BanditRLProof.Tsallis.sum_prob_mul_linearLoss_sub_next_importanceWeightedLoss_le_refined_of_shiftedTaylor theorem Tsallis-FTRL BanditRLProof.TsallisRefinedImportanceWeightedMoment Compiled BanditRLProof/TsallisRefinedImportanceWeightedMoment.lean:399
BanditRLProof.Tsallis.probability_le_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisRefinedSuboptimalStability Compiled BanditRLProof/TsallisRefinedSuboptimalStability.lean:24
BanditRLProof.Tsallis.sqrt_mul_one_sub_le_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisRefinedSuboptimalStability Compiled BanditRLProof/TsallisRefinedSuboptimalStability.lean:31
BanditRLProof.Tsallis.sqrt_mul_one_sub_le_one_sub theorem Tsallis-FTRL BanditRLProof.TsallisRefinedSuboptimalStability Compiled BanditRLProof/TsallisRefinedSuboptimalStability.lean:38
BanditRLProof.Tsallis.one_sub_eq_sum_erase theorem Tsallis-FTRL BanditRLProof.TsallisRefinedSuboptimalStability Compiled BanditRLProof/TsallisRefinedSuboptimalStability.lean:47
BanditRLProof.Tsallis.sum_sqrt_mul_one_sub_le_two_mul_sum_erase_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisRefinedSuboptimalStability Compiled BanditRLProof/TsallisRefinedSuboptimalStability.lean:60
BanditRLProof.Tsallis.regret_le_of_refinedHalfPowerSelfBounding theorem Tsallis-FTRL BanditRLProof.TsallisRefinedSuboptimalStability Compiled BanditRLProof/TsallisRefinedSuboptimalStability.lean:100
BanditRLProof.Tsallis.powerSum definition Tsallis-FTRL BanditRLProof.TsallisRegularizer Compiled BanditRLProof/TsallisRegularizer.lean:24
BanditRLProof.Tsallis.entropy definition Tsallis-FTRL BanditRLProof.TsallisRegularizer Compiled BanditRLProof/TsallisRegularizer.lean:29
BanditRLProof.Tsallis.negEntropyRegularizer definition Tsallis-FTRL BanditRLProof.TsallisRegularizer Compiled BanditRLProof/TsallisRegularizer.lean:34
BanditRLProof.Tsallis.one_sub_exponent_ne_zero theorem Tsallis-FTRL BanditRLProof.TsallisRegularizer Compiled BanditRLProof/TsallisRegularizer.lean:39
BanditRLProof.Tsallis.powerSum_nonneg_of_finiteSimplex theorem Tsallis-FTRL BanditRLProof.TsallisRegularizer Compiled BanditRLProof/TsallisRegularizer.lean:47
BanditRLProof.Tsallis.negEntropyRegularizer_wellDefined_on_finiteSimplex theorem Tsallis-FTRL BanditRLProof.TsallisRegularizer Compiled BanditRLProof/TsallisRegularizer.lean:60
BanditRLProof.Tsallis.halfTsallisPotentialStability_le_linearLoss_sub_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:22
BanditRLProof.Tsallis.halfTsallisPotentialStability_importanceWeightedLoss_le_one_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:72
BanditRLProof.Tsallis.sum_prob_mul_halfTsallisPotentialStability_importanceWeightedLoss_le_one_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:113
BanditRLProof.Tsallis.integrable_importanceWeightedPotentialStabilityScore_finiteActionKernel_coarse theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:151
BanditRLProof.Tsallis.integral_importanceWeightedPotentialStabilityScore_le_integral_one_of_condDistrib_of_minimizers theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:245
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisSuccessorPotentialStabilityAtTime_le_one theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:335
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisSuccessorPotentialStabilityAtTime_le_refined theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:497
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisInitialPotentialStabilityAtTime_le_one theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:658
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSuccessorAllRatePotentialStabilityBoundAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:794
BanditRLProof.Tsallis.sampledScheduledHalfTsallisInitialAllRatePotentialStabilityBound definition Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:804
BanditRLProof.Tsallis.sampledScheduledHalfTsallisAllRatePotentialStabilityBoundAtTime definition Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:814
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisSuccessorPotentialStabilityAtTime_le_allRateBound theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:826
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisInitialPotentialStabilityAtTime_le_allRateBound theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:897
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPotentialStabilityAtTime_le_allRateBound theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:973
BanditRLProof.Tsallis.integrable_sum_sampledScheduledHalfTsallisPotentialStabilityAtTime_allRate theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:1013
BanditRLProof.Tsallis.integral_sum_sampledScheduledHalfTsallisPotentialStabilityAtTime_le_allRateBound theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllRateExpectedStability Compiled BanditRLProof/TsallisScheduledAllRateExpectedStability.lean:1063
BanditRLProof.Tsallis.integrable_sampledScheduledHalfTsallisSuccessorPotentialStabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllTimesExpectedStability Compiled BanditRLProof/TsallisScheduledAllTimesExpectedStability.lean:23
BanditRLProof.Tsallis.integrable_sum_sampledScheduledHalfTsallisSuccessorPotentialStabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllTimesExpectedStability Compiled BanditRLProof/TsallisScheduledAllTimesExpectedStability.lean:98
BanditRLProof.Tsallis.integrable_sum_sampledScheduledHalfTsallisPotentialStabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllTimesExpectedStability Compiled BanditRLProof/TsallisScheduledAllTimesExpectedStability.lean:135
BanditRLProof.Tsallis.integral_sum_sampledScheduledHalfTsallisPotentialStabilityAtTime_le_refined theorem Tsallis-FTRL BanditRLProof.TsallisScheduledAllTimesExpectedStability Compiled BanditRLProof/TsallisScheduledAllTimesExpectedStability.lean:179
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPastSigma definition Tsallis-FTRL BanditRLProof.TsallisScheduledConditionalMeanGap Compiled BanditRLProof/TsallisScheduledConditionalMeanGap.lean:23
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPastSigma_le theorem Tsallis-FTRL BanditRLProof.TsallisScheduledConditionalMeanGap Compiled BanditRLProof/TsallisScheduledConditionalMeanGap.lean:35
BanditRLProof.Tsallis.measurable_sampledScheduledHalfTsallisProbabilityAtTime_pastSigma theorem Tsallis-FTRL BanditRLProof.TsallisScheduledConditionalMeanGap Compiled BanditRLProof/TsallisScheduledConditionalMeanGap.lean:48
BanditRLProof.Tsallis.HasScheduledConditionalMeanGapLaw definition Tsallis-FTRL BanditRLProof.TsallisScheduledConditionalMeanGap Compiled BanditRLProof/TsallisScheduledConditionalMeanGap.lean:79
BanditRLProof.Tsallis.hasScheduledExpectedGapLaw_of_conditionalMeanGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledConditionalMeanGap Compiled BanditRLProof/TsallisScheduledConditionalMeanGap.lean:98
BanditRLProof.Tsallis.HasScheduledExpectedGapLaw definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedGapSelfBounding Compiled BanditRLProof/TsallisScheduledExpectedGapSelfBounding.lean:23
BanditRLProof.Tsallis.integrable_sampledScheduledHalfTsallisProbability_mul_predictableLossDiffAt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedGapSelfBounding Compiled BanditRLProof/TsallisScheduledExpectedGapSelfBounding.lean:40
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_eq_weightedLossGapMass theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedGapSelfBounding Compiled BanditRLProof/TsallisScheduledExpectedGapSelfBounding.lean:77
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_eq_suboptimalExpectedGapMass_of_expectedGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedGapSelfBounding Compiled BanditRLProof/TsallisScheduledExpectedGapSelfBounding.lean:109
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_hasSelfBounding_of_expectedGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedGapSelfBounding Compiled BanditRLProof/TsallisScheduledExpectedGapSelfBounding.lean:159
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableEstimatedLossAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:22
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableEnvironmentRegret definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:35
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableEstimatedRegret definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:51
BanditRLProof.Tsallis.measurable_sampledScheduledHalfTsallisProbabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:68
BanditRLProof.Tsallis.measurable_sampledScheduledHalfTsallisPredictableEstimatedLossAt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:93
BanditRLProof.Tsallis.sampledScheduledHalfTsallisObservedEstimatedLossAt_eq_predictable_ae theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:116
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableEstimatedLossAt_first_moments theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:170
BanditRLProof.Tsallis.finiteSimplex_sampledScheduledHalfTsallisProbabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:347
BanditRLProof.Tsallis.integrable_sampledScheduledHalfTsallisPredictableLinearLossAt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:369
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEstimatedRegret_eq_environmentRegret theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:459
BanditRLProof.Tsallis.sampledScheduledHalfTsallisEstimatedRegret_eq_predictable_ae theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:555
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisEstimatedRegret_eq_environmentRegret theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:597
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_allRateBound theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedRegret Compiled BanditRLProof/TsallisScheduledExpectedRegret.lean:648
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHistoryAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:25
BanditRLProof.Tsallis.sampledScheduledHalfTsallisActionAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:32
BanditRLProof.Tsallis.sampledScheduledHalfTsallisScoreAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:38
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableLossAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:47
BanditRLProof.Tsallis.sampledScheduledHalfTsallisProbabilityAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:55
BanditRLProof.Tsallis.sampledScheduledHalfTsallisUpdatedAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:64
BanditRLProof.Tsallis.sampledScheduledHalfTsallisEnvironmentHistoryDistributionSource definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:77
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPolicyAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:97
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPolicyAt_eq_finiteActionKernel theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:126
BanditRLProof.Tsallis.HalfTsallisScheduleGeneratedSelectorMeasurability structure Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:149
BanditRLProof.Tsallis.measurable_sampledScheduledHalfTsallisUpdatedAt_canonical theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:165
BanditRLProof.Tsallis.canonicalHalfTsallisScheduleGeneratedSelectorMeasurability definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:236
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHistoryActionPotentialStabilityAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:253
BanditRLProof.Tsallis.sampledScheduledHalfTsallisRefinedPotentialStabilityBoundAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:266
BanditRLProof.Tsallis.measurable_sampledScheduledHalfTsallisHistoryActionPotentialStabilityAt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:275
BanditRLProof.Tsallis.integrable_sampledScheduledHalfTsallisRefinedPotentialStabilityBoundAt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:303
BanditRLProof.Tsallis.integrable_sampledScheduledHalfTsallisHistoryActionPotentialStabilityAt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:327
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPotentialStabilityAtTime_succ_eq_historyAction_ae theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:384
BanditRLProof.Tsallis.integral_sum_sampledScheduledHalfTsallisSuccessorPotentialStabilityAtTime_le_refined theorem Tsallis-FTRL BanditRLProof.TsallisScheduledExpectedStability Compiled BanditRLProof/TsallisScheduledExpectedStability.lean:479
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableSuboptimalGapMass definition Tsallis-FTRL BanditRLProof.TsallisScheduledFixedGapSelfBounding Compiled BanditRLProof/TsallisScheduledFixedGapSelfBounding.lean:20
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_eq_suboptimalGapMass theorem Tsallis-FTRL BanditRLProof.TsallisScheduledFixedGapSelfBounding Compiled BanditRLProof/TsallisScheduledFixedGapSelfBounding.lean:33
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableSuboptimalGapMass_eq theorem Tsallis-FTRL BanditRLProof.TsallisScheduledFixedGapSelfBounding Compiled BanditRLProof/TsallisScheduledFixedGapSelfBounding.lean:67
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_eq_suboptimalExpectedGapMass theorem Tsallis-FTRL BanditRLProof.TsallisScheduledFixedGapSelfBounding Compiled BanditRLProof/TsallisScheduledFixedGapSelfBounding.lean:110
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_hasSelfBounding_of_fixedGap theorem Tsallis-FTRL BanditRLProof.TsallisScheduledFixedGapSelfBounding Compiled BanditRLProof/TsallisScheduledFixedGapSelfBounding.lean:160
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_of_fixedGap theorem Tsallis-FTRL BanditRLProof.TsallisScheduledFixedGapSelfBounding Compiled BanditRLProof/TsallisScheduledFixedGapSelfBounding.lean:194
BanditRLProof.Tsallis.HasIIDStateCoordinateLocality structure Tsallis-FTRL BanditRLProof.TsallisScheduledIIDHistoryAdaptive Compiled BanditRLProof/TsallisScheduledIIDHistoryAdaptive.lean:22
BanditRLProof.Tsallis.sampledScheduledHalfTsallisTrajectoryKernel_map_frestrictLe_eq_of_iidStateCoordinateLocality_prefix_eq theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDHistoryAdaptive Compiled BanditRLProof/TsallisScheduledIIDHistoryAdaptive.lean:36
BanditRLProof.Tsallis.sampledScheduledHalfTsallisIIDHistoryAdaptivePrefixKernel definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDHistoryAdaptive Compiled BanditRLProof/TsallisScheduledIIDHistoryAdaptive.lean:92
BanditRLProof.Tsallis.hasScheduledIIDPrefixKernelFactorization_sampledScheduledHalfTsallisHistoryAdaptiveTrajectoryKernel theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDHistoryAdaptive Compiled BanditRLProof/TsallisScheduledIIDHistoryAdaptive.lean:134
BanditRLProof.Tsallis.iidLossStatePredictableLossVector definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:25
BanditRLProof.Tsallis.predictableLossAt_iidLossStatePredictableLossVector theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:61
BanditRLProof.Tsallis.extendLossStatePrefix definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:80
BanditRLProof.Tsallis.measurable_extendLossStatePrefix theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:86
BanditRLProof.Tsallis.extendLossStatePrefix_apply_of_le theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:98
BanditRLProof.Tsallis.sampledScheduledHalfTsallisTrajectoryKernel_map_frestrictLe_eq_of_iidLossState_prefix_eq theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:108
BanditRLProof.Tsallis.sampledScheduledHalfTsallisIIDPrefixKernel definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:171
BanditRLProof.Tsallis.iidLossStateMeanGap definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:225
BanditRLProof.Tsallis.HasScheduledIIDPrefixKernelFactorization definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:235
BanditRLProof.Tsallis.hasScheduledIIDPrefixKernelFactorization_sampledScheduledHalfTsallisTrajectoryKernel theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:252
BanditRLProof.Tsallis.hasScheduledIndependentMeanGapLaw_of_iidLossState theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:324
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_log_iidLossState theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDMeanGap Compiled BanditRLProof/TsallisScheduledIIDMeanGap.lean:498
BanditRLProof.Tsallis.iidTimeVaryingLossStatePredictableLossVector definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDTimeVaryingMeanGap Compiled BanditRLProof/TsallisScheduledIIDTimeVaryingMeanGap.lean:21
BanditRLProof.Tsallis.predictableLossAt_iidTimeVaryingLossStatePredictableLossVector theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDTimeVaryingMeanGap Compiled BanditRLProof/TsallisScheduledIIDTimeVaryingMeanGap.lean:58
BanditRLProof.Tsallis.sampledScheduledHalfTsallisTrajectoryKernel_map_frestrictLe_eq_of_iidTimeVaryingLossState_prefix_eq theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDTimeVaryingMeanGap Compiled BanditRLProof/TsallisScheduledIIDTimeVaryingMeanGap.lean:77
BanditRLProof.Tsallis.sampledScheduledHalfTsallisIIDTimeVaryingPrefixKernel definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDTimeVaryingMeanGap Compiled BanditRLProof/TsallisScheduledIIDTimeVaryingMeanGap.lean:141
BanditRLProof.Tsallis.hasScheduledIIDPrefixKernelFactorization_sampledScheduledHalfTsallisTimeVaryingTrajectoryKernel theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDTimeVaryingMeanGap Compiled BanditRLProof/TsallisScheduledIIDTimeVaryingMeanGap.lean:195
BanditRLProof.Tsallis.independentLossStateTimeVaryingMeanGap definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDTimeVaryingMeanGap Compiled BanditRLProof/TsallisScheduledIIDTimeVaryingMeanGap.lean:267
BanditRLProof.Tsallis.iidLossStateTimeVaryingMeanGap definition Tsallis-FTRL BanditRLProof.TsallisScheduledIIDTimeVaryingMeanGap Compiled BanditRLProof/TsallisScheduledIIDTimeVaryingMeanGap.lean:276
BanditRLProof.Tsallis.hasScheduledTimeVaryingIndependentMeanGapLaw_of_independentLossState theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDTimeVaryingMeanGap Compiled BanditRLProof/TsallisScheduledIIDTimeVaryingMeanGap.lean:286
BanditRLProof.Tsallis.hasScheduledTimeVaryingIndependentMeanGapLaw_of_iidLossState theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIIDTimeVaryingMeanGap Compiled BanditRLProof/TsallisScheduledIIDTimeVaryingMeanGap.lean:464
BanditRLProof.Tsallis.HasScheduledIndependentMeanGapLaw definition Tsallis-FTRL BanditRLProof.TsallisScheduledIndependentMeanGap Compiled BanditRLProof/TsallisScheduledIndependentMeanGap.lean:24
BanditRLProof.Tsallis.hasScheduledConditionalMeanGapLaw_of_independentMeanGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIndependentMeanGap Compiled BanditRLProof/TsallisScheduledIndependentMeanGap.lean:41
BanditRLProof.Tsallis.hasScheduledExpectedGapLaw_of_independentMeanGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIndependentMeanGap Compiled BanditRLProof/TsallisScheduledIndependentMeanGap.lean:98
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_log_independentMeanGap theorem Tsallis-FTRL BanditRLProof.TsallisScheduledIndependentMeanGap Compiled BanditRLProof/TsallisScheduledIndependentMeanGap.lean:120
BanditRLProof.Tsallis.sampledScheduledHalfTsallisInitialHistoryActionPotentialStability definition Tsallis-FTRL BanditRLProof.TsallisScheduledInitialExpectedStability Compiled BanditRLProof/TsallisScheduledInitialExpectedStability.lean:23
BanditRLProof.Tsallis.sampledScheduledHalfTsallisInitialRefinedPotentialStabilityBound definition Tsallis-FTRL BanditRLProof.TsallisScheduledInitialExpectedStability Compiled BanditRLProof/TsallisScheduledInitialExpectedStability.lean:35
BanditRLProof.Tsallis.measurable_sampledScheduledHalfTsallisInitialHistoryActionPotentialStability theorem Tsallis-FTRL BanditRLProof.TsallisScheduledInitialExpectedStability Compiled BanditRLProof/TsallisScheduledInitialExpectedStability.lean:44
BanditRLProof.Tsallis.integrable_sampledScheduledHalfTsallisInitialRefinedPotentialStabilityBound theorem Tsallis-FTRL BanditRLProof.TsallisScheduledInitialExpectedStability Compiled BanditRLProof/TsallisScheduledInitialExpectedStability.lean:69
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPotentialStabilityAtTime_zero_eq_initial_ae theorem Tsallis-FTRL BanditRLProof.TsallisScheduledInitialExpectedStability Compiled BanditRLProof/TsallisScheduledInitialExpectedStability.lean:89
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisInitialPotentialStabilityAtTime_le_refined theorem Tsallis-FTRL BanditRLProof.TsallisScheduledInitialExpectedStability Compiled BanditRLProof/TsallisScheduledInitialExpectedStability.lean:164
BanditRLProof.Tsallis.HalfTsallisScheduleFiniteHistorySelectorMeasurability structure Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:24
BanditRLProof.Tsallis.canonicalHalfTsallisScheduleFiniteHistorySelectorMeasurability definition Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:33
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHistoryScore definition Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:42
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHistoryScore_zero theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:62
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHistoryScore_succ theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:74
BanditRLProof.Tsallis.measurable_sampledScheduledHalfTsallisHistoryScore theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:93
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHistoryDistribution definition Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:173
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHistoryDistributionSource definition Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:182
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHistoryAlgorithm definition Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:205
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHistoryAlgorithm_policy theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:229
BanditRLProof.Tsallis.sampledScheduledHalfTsallisTrajectoryKernel definition Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:245
BanditRLProof.Tsallis.sampledScheduledHalfTsallisTrajectoryMeasure_condDistrib_action theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:276
BanditRLProof.Tsallis.sampledScheduledHalfTsallisTrajectoryMeasure_condDistrib_action_given_environment theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRecursiveTrajectory Compiled BanditRLProof/TsallisScheduledRecursiveTrajectory.lean:310
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_hasSelfBounding_of_referenceExpectedGapLaw_of_expectedDeviation theorem Tsallis-FTRL BanditRLProof.TsallisScheduledReferenceGapExpectedDeviationSelfBounding Compiled BanditRLProof/TsallisScheduledReferenceGapExpectedDeviationSelfBounding.lean:22
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_hasSelfBounding_of_referenceExpectedGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledReferenceGapSelfBounding Compiled BanditRLProof/TsallisScheduledReferenceGapSelfBounding.lean:22
BanditRLProof.Tsallis.sqrt_sub_self_le_half_one_sub theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedExpectedPenalty Compiled BanditRLProof/TsallisScheduledRefinedExpectedPenalty.lean:21
BanditRLProof.Tsallis.halfTsallisPotentialMass_sub_one_le_two_mul_sum_erase_refined theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedExpectedPenalty Compiled BanditRLProof/TsallisScheduledRefinedExpectedPenalty.lean:29
BanditRLProof.Tsallis.sum_sampledScheduledHalfTsallisPotentialPenalty_pointMass_le_refined theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedExpectedPenalty Compiled BanditRLProof/TsallisScheduledRefinedExpectedPenalty.lean:57
BanditRLProof.Tsallis.sampledScheduledHalfTsallisRefinedSuboptimalMassAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedExpectedPenalty Compiled BanditRLProof/TsallisScheduledRefinedExpectedPenalty.lean:196
BanditRLProof.Tsallis.sampledScheduledHalfTsallisExpectedRefinedSuboptimalMassAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedExpectedPenalty Compiled BanditRLProof/TsallisScheduledRefinedExpectedPenalty.lean:208
BanditRLProof.Tsallis.integrable_sampledScheduledHalfTsallisRefinedSuboptimalMassAt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedExpectedPenalty Compiled BanditRLProof/TsallisScheduledRefinedExpectedPenalty.lean:220
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisRefinedSuboptimalMassAt_le_expected theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedExpectedPenalty Compiled BanditRLProof/TsallisScheduledRefinedExpectedPenalty.lean:247
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_refinedExpectedPenalty theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedExpectedPenalty Compiled BanditRLProof/TsallisScheduledRefinedExpectedPenalty.lean:292
BanditRLProof.Tsallis.sampledScheduledHalfTsallisExpectedSuboptimalSqrtMassAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedStabilityPenalty Compiled BanditRLProof/TsallisScheduledRefinedStabilityPenalty.lean:21
BanditRLProof.Tsallis.sampledScheduledHalfTsallisExpectedRefinedSuboptimalMassAt_le_sqrtMass theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedStabilityPenalty Compiled BanditRLProof/TsallisScheduledRefinedStabilityPenalty.lean:33
BanditRLProof.Tsallis.sampledScheduledHalfTsallisRefinedCoefficient definition Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedStabilityPenalty Compiled BanditRLProof/TsallisScheduledRefinedStabilityPenalty.lean:58
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_refinedStabilityPenalty theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedStabilityPenalty Compiled BanditRLProof/TsallisScheduledRefinedStabilityPenalty.lean:66
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_refinedStabilityPenalty_of_selfBounding theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedStabilityPenalty Compiled BanditRLProof/TsallisScheduledRefinedStabilityPenalty.lean:220
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_refinedStabilityPenalty_of_fixedGap theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedStabilityPenalty Compiled BanditRLProof/TsallisScheduledRefinedStabilityPenalty.lean:316
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_refinedStabilityPenalty_of_expectedGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledRefinedStabilityPenalty Compiled BanditRLProof/TsallisScheduledRefinedStabilityPenalty.lean:357
BanditRLProof.Tsallis.sampledScheduledHalfTsallisProbabilityAtTime definition Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:23
BanditRLProof.Tsallis.sampledScheduledHalfTsallisObservedEstimatedLossAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:33
BanditRLProof.Tsallis.cumulativeLoss_sampledScheduledHalfTsallisObservedEstimatedLossAt_succ theorem Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:44
BanditRLProof.Tsallis.halfTsallisScheduledMinimizer_observedEstimatedLoss_eq_probabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:75
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSameRateNextAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:99
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPotentialStabilityAtTime definition Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:110
BanditRLProof.Tsallis.sampledScheduledHalfTsallisPotentialPenaltyAtTime definition Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:126
BanditRLProof.Tsallis.sampledScheduledHalfTsallisEstimatedRegret definition Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:146
BanditRLProof.Tsallis.sampledScheduledHalfTsallisEstimatedRegret_eq_stability_add_penalty theorem Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:163
BanditRLProof.Tsallis.sum_sampledScheduledHalfTsallisPotentialPenalty_pointMass_le theorem Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:188
BanditRLProof.Tsallis.sampledScheduledHalfTsallisEstimatedRegret_pointMass_le_stability_add_penalty theorem Tsallis-FTRL BanditRLProof.TsallisScheduledScoreAlignment Compiled BanditRLProof/TsallisScheduledScoreAlignment.lean:213
BanditRLProof.Tsallis.regret_le_selfBoundingInterpolation theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSelfBoundingInterpolation Compiled BanditRLProof/TsallisScheduledSelfBoundingInterpolation.lean:21
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_selfBoundingInterpolation theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSelfBoundingInterpolation Compiled BanditRLProof/TsallisScheduledSelfBoundingInterpolation.lean:46
BanditRLProof.Tsallis.sum_sampledScheduledHalfTsallisExpectedProbability_le_quadraticFilterSplit theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSelfBoundingOptimization Compiled BanditRLProof/TsallisScheduledSelfBoundingOptimization.lean:23
BanditRLProof.Tsallis.sum_range_sampledScheduledHalfTsallisExpectedProbability_le_quadraticPrefixSplit theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSelfBoundingOptimization Compiled BanditRLProof/TsallisScheduledSelfBoundingOptimization.lean:116
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_selfBoundingQuadraticSplit theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSelfBoundingOptimization Compiled BanditRLProof/TsallisScheduledSelfBoundingOptimization.lean:194
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_refinedSelfBoundingQuadraticSum_of_refinedCoefficient_le theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSelfBoundingOptimization Compiled BanditRLProof/TsallisScheduledSelfBoundingOptimization.lean:363
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_refinedSelfBoundingQuadraticSplit_of_refinedCoefficient_le theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSelfBoundingOptimization Compiled BanditRLProof/TsallisScheduledSelfBoundingOptimization.lean:514
BanditRLProof.Tsallis.sampledScheduledHalfTsallisExpectedProbabilityAt definition Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:23
BanditRLProof.Tsallis.integrable_sampledScheduledHalfTsallisProbabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:33
BanditRLProof.Tsallis.integrable_sqrt_sampledScheduledHalfTsallisProbabilityAtTime theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:53
BanditRLProof.Tsallis.finiteSimplex_sampledScheduledHalfTsallisExpectedProbabilityAt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:78
BanditRLProof.Tsallis.integral_sqrt_sampledScheduledHalfTsallisProbabilityAtTime_le_sqrt_expected theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:115
BanditRLProof.Tsallis.sampledScheduledHalfTsallisAllRatePotentialStabilityBoundAtTime_eq_refined theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:149
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisAllRatePotentialStabilityBoundAtTime_le_suboptimalExpectedSqrt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:184
BanditRLProof.Tsallis.integral_sum_sampledScheduledHalfTsallisAllRatePotentialStabilityBoundAtTime_le_suboptimalExpectedSqrt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:288
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_suboptimalExpectedSqrt theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:354
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_of_selfBounding theorem Tsallis-FTRL BanditRLProof.TsallisScheduledSuboptimalExpectedBound Compiled BanditRLProof/TsallisScheduledSuboptimalExpectedBound.lean:399
BanditRLProof.Tsallis.HasScheduledTimeVaryingExpectedGapLaw definition Tsallis-FTRL BanditRLProof.TsallisScheduledTimeVaryingExpectedGap Compiled BanditRLProof/TsallisScheduledTimeVaryingExpectedGap.lean:22
BanditRLProof.Tsallis.HasScheduledTimeVaryingConditionalMeanGapLaw definition Tsallis-FTRL BanditRLProof.TsallisScheduledTimeVaryingExpectedGap Compiled BanditRLProof/TsallisScheduledTimeVaryingExpectedGap.lean:40
BanditRLProof.Tsallis.HasScheduledTimeVaryingIndependentMeanGapLaw definition Tsallis-FTRL BanditRLProof.TsallisScheduledTimeVaryingExpectedGap Compiled BanditRLProof/TsallisScheduledTimeVaryingExpectedGap.lean:57
BanditRLProof.Tsallis.hasScheduledTimeVaryingConditionalMeanGapLaw_of_independentMeanGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledTimeVaryingExpectedGap Compiled BanditRLProof/TsallisScheduledTimeVaryingExpectedGap.lean:74
BanditRLProof.Tsallis.hasScheduledTimeVaryingExpectedGapLaw_of_conditionalMeanGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledTimeVaryingExpectedGap Compiled BanditRLProof/TsallisScheduledTimeVaryingExpectedGap.lean:123
BanditRLProof.Tsallis.hasScheduledTimeVaryingExpectedGapLaw_of_independentMeanGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledTimeVaryingExpectedGap Compiled BanditRLProof/TsallisScheduledTimeVaryingExpectedGap.lean:201
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_eq_suboptimalTimeVaryingExpectedGapMass theorem Tsallis-FTRL BanditRLProof.TsallisScheduledTimeVaryingExpectedGap Compiled BanditRLProof/TsallisScheduledTimeVaryingExpectedGap.lean:222
BanditRLProof.Tsallis.scheduledTimeVaryingGapDeviationBudget definition Tsallis-FTRL BanditRLProof.TsallisScheduledTimeVaryingExpectedGap Compiled BanditRLProof/TsallisScheduledTimeVaryingExpectedGap.lean:271
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_hasSelfBounding_of_timeVaryingPerturbedExpectedGapLaw theorem Tsallis-FTRL BanditRLProof.TsallisScheduledTimeVaryingExpectedGap Compiled BanditRLProof/TsallisScheduledTimeVaryingExpectedGap.lean:280
BanditRLProof.Tsallis.pointMass definition Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:27
BanditRLProof.Tsallis.finiteSimplex_pointMass theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:31
BanditRLProof.Tsallis.linearLoss_pointMass theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:40
BanditRLProof.Tsallis.linearLoss_sub_pointMass_eq_gapMass theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:49
BanditRLProof.Tsallis.sampledHalfTsallisPredictableGapMass definition Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:78
BanditRLProof.Tsallis.HasSelfBoundingRegret definition Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:89
BanditRLProof.Tsallis.sampledHalfTsallisPredictableEnvironmentRegret_pointMass_eq_gapMass theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:94
BanditRLProof.Tsallis.integral_sampledHalfTsallisPredictableEnvironmentRegret_hasSelfBounding theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:123
BanditRLProof.Tsallis.integral_sampledHalfTsallisPredictableEnvironmentRegret_pointMass_le theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:170
BanditRLProof.Tsallis.two_mul_coeff_mul_sqrt_sub_gap_mul_le_sq_div_gap theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:200
BanditRLProof.Tsallis.regret_le_two_mul_base_add_sum_sq_div_gap_add_corruption theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:221
BanditRLProof.Tsallis.powerSum_pointMass_half theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:268
BanditRLProof.Tsallis.sum_erase_sqrt_pointMass theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:275
BanditRLProof.Tsallis.not_forall_powerSum_half_le_sum_erase_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisSelfBounding Compiled BanditRLProof/TsallisSelfBounding.lean:288
BanditRLProof.Tsallis.selfBoundingBetaEquation definition Tsallis-FTRL BanditRLProof.TsallisSelfBoundingBetaRoot Compiled BanditRLProof/TsallisSelfBoundingBetaRoot.lean:19
BanditRLProof.Tsallis.continuousOn_selfBoundingBetaEquation theorem Tsallis-FTRL BanditRLProof.TsallisSelfBoundingBetaRoot Compiled BanditRLProof/TsallisSelfBoundingBetaRoot.lean:24
BanditRLProof.Tsallis.exists_selfBoundingBetaEquation_eq_zero theorem Tsallis-FTRL BanditRLProof.TsallisSelfBoundingBetaRoot Compiled BanditRLProof/TsallisSelfBoundingBetaRoot.lean:41
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSqrtSchedule definition Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:20
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHarmonicBudget definition Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:24
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHarmonicBudget_eq_harmonic theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:31
BanditRLProof.Tsallis.sampledScheduledHalfTsallisHarmonicBudget_le_one_add_log theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:43
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSqrtSchedule_pos theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:50
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSqrtSchedule_le_half theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:55
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSqrtSchedule_succ_le theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:65
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSqrtSchedule_four_mul_sq theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:79
BanditRLProof.Tsallis.sqrt_succ_sub_sqrt_le_one_div_sqrt_succ theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:92
BanditRLProof.Tsallis.sampledScheduledHalfTsallisRefinedCoefficient_sqrtSchedule_nonneg theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:116
BanditRLProof.Tsallis.sampledScheduledHalfTsallisRefinedCoefficient_sqrtSchedule_le theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:132
BanditRLProof.Tsallis.sampledScheduledHalfTsallisRefinedCoefficient_sqrtSchedule_sq_le theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:156
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_of_selfBounding theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:179
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_fixedGap theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:304
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_expectedGap theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:341
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_log_fixedGap theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:385
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_log_expectedGap theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleFixedGap Compiled BanditRLProof/TsallisSqrtScheduleFixedGap.lean:457
BanditRLProof.Tsallis.sum_range_one_div_sqrt_natSucc_le_two_sqrt theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingOptimization Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingOptimization.lean:21
BanditRLProof.Tsallis.sum_Ico_one_div_natSucc_le_log_div theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingOptimization Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingOptimization.lean:56
BanditRLProof.Tsallis.sum_range_sqrtSchedule_activeBranch_le_closedForm theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingOptimization Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingOptimization.lean:83
BanditRLProof.Tsallis.sum_Ico_sqrtSchedule_unconstrainedBranch_le_log theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingOptimization Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingOptimization.lean:117
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_refinedSelfBoundingQuadraticSplit theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingOptimization Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingOptimization.lean:151
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_refinedSelfBoundingQuadraticPrefixSplit theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingOptimization Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingOptimization.lean:261
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_refinedSelfBoundingQuadraticClosedForm theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingOptimization Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingOptimization.lean:410
BanditRLProof.Tsallis.refinedLocalBetaEquation definition Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:19
BanditRLProof.Tsallis.continuousOn_refinedLocalBetaEquation theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:25
BanditRLProof.Tsallis.sq_sqrt_sub_one_le_sub_log_sub_one theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:39
BanditRLProof.Tsallis.refinedLocalBetaWeight_bounds_of_eq_zero theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:56
BanditRLProof.Tsallis.exists_refinedLocalBetaEquation_eq_zero theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:125
BanditRLProof.Tsallis.exists_refinedLocalBetaEquation_eq_zero_and_weight_bounds theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:178
BanditRLProof.Tsallis.refinedLocalAlpha definition Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:208
BanditRLProof.Tsallis.refinedLocalLambda definition Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:213
BanditRLProof.Tsallis.refinedLocalAlpha_sq theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:218
BanditRLProof.Tsallis.refinedLocalAlpha_pos theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:227
BanditRLProof.Tsallis.refinedLocalAlpha_le_one theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:236
BanditRLProof.Tsallis.refinedLocalLambda_mem_Ioc theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:249
BanditRLProof.Tsallis.one_add_refinedLocalLambda_eq theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:269
BanditRLProof.Tsallis.two_mul_refinedLocalLambda_div_one_add_eq_alpha theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedScalar Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedScalar.lean:279
BanditRLProof.Tsallis.sum_one_div_lambda_mul_eq_div theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedTuning.lean:18
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSelfBoundingThreshold_refinedLocalLambda_eq theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedTuning.lean:37
BanditRLProof.Tsallis.refinedLocalTunedRegretBound definition Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedTuning.lean:146
BanditRLProof.Tsallis.refinedLocalTunedRegretBound_le_explicit theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedTuning.lean:155
BanditRLProof.Tsallis.exists_integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_refinedLocalTuned theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedTuning.lean:348
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_refinedLocalExplicit theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedTuning.lean:527
BanditRLProof.Tsallis.RefinedLocalCorruptionWindow definition Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedWindow Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedWindow.lean:13
BanditRLProof.Tsallis.refinedLocalCorruptionWindow_scalar_bounds theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingRefinedWindow Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingRefinedWindow.lean:25
BanditRLProof.Tsallis.natFloor_positive_and_half_le theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingTuning.lean:23
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSelfBoundingThreshold definition Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingTuning.lean:38
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_refinedSelfBoundingFloorCutoff theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingTuning.lean:50
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSelfBoundingOneThreshold definition Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingTuning.lean:235
BanditRLProof.Tsallis.sampledScheduledHalfTsallisSelfBoundingOneThreshold_eq theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingTuning.lean:243
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_selfBoundingOne theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingTuning.lean:266
BanditRLProof.Tsallis.integral_sampledScheduledHalfTsallisPredictableEnvironmentRegret_pointMass_le_sqrtSchedule_selfBoundingOne_explicit theorem Tsallis-FTRL BanditRLProof.TsallisSqrtScheduleSelfBoundingTuning Compiled BanditRLProof/TsallisSqrtScheduleSelfBoundingTuning.lean:347
BanditRLProof.Tsallis.halfTsallisPotentialMass definition Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:28
BanditRLProof.Tsallis.halfTsallisPotentialMass_eq_two_mul_powerSum_sub_one theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:33
BanditRLProof.Tsallis.halfTsallisPotentialMass_pointMass theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:42
BanditRLProof.Tsallis.halfTsallisPotentialValue_eq_neg_linearLoss_add_mass_div theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:51
BanditRLProof.Tsallis.halfTsallisPotentialValue_le_of_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:63
BanditRLProof.Tsallis.halfTsallisPotentialValue_new_sub_old_le_rateChange_mul_mass theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:85
BanditRLProof.Tsallis.halfTsallisPotentialMass_le_of_zero_isRegularizedMinimizer theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:114
BanditRLProof.Tsallis.sum_range_succ_sub_eq_first_sub_last_add_cross theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:133
BanditRLProof.Tsallis.halfTsallisScheduledMinimizer definition Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:145
BanditRLProof.Tsallis.halfTsallisScheduledSameRateNext definition Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:153
BanditRLProof.Tsallis.sum_halfTsallisScheduledPotentialPenalty_le theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:162
BanditRLProof.Tsallis.sum_halfTsallisScheduledPotentialPenalty_le_initial_sub_comparator_div theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:282
BanditRLProof.Tsallis.sum_halfTsallisCanonicalScheduledPotentialPenalty_le theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:370
BanditRLProof.Tsallis.sum_halfTsallisCanonicalScheduledPotentialPenalty_pointMass_le theorem Tsallis-FTRL BanditRLProof.TsallisTimeVaryingPenalty Compiled BanditRLProof/TsallisTimeVaryingPenalty.lean:404
BanditRLProof.UCBSummability.finiteHorizonBadEvent definition UCB BanditRLProof.UCBSummability Compiled BanditRLProof/UCBSummability.lean:19
BanditRLProof.UCBSummability.measure_finiteHorizonBadEvent_le_sum theorem UCB BanditRLProof.UCBSummability Compiled BanditRLProof/UCBSummability.lean:30
BanditRLProof.UCBSummability.measure_finiteHorizonBadEvent_le_tail_sum theorem UCB BanditRLProof.UCBSummability Compiled BanditRLProof/UCBSummability.lean:58
BanditRLProof.tsum_natSuccSquare_mul_stoppingFiberMeasure_eq_lintegral_rounds_sq theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:26
BanditRLProof.tsum_natSuccSquare_mul_stoppingFiberMeasure_ne_top theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:89
BanditRLProof.tsum_natSuccSquare_mul_stoppingFiberRealMeasure_eq_integral_rounds_sq theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:112
BanditRLProof.summable_sqrt_stoppingFiberRealMeasure_of_memLp_two theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:153
BanditRLProof.tsum_sqrt_stoppingFiberRealMeasure_le_half_mul_integral_rounds_sq_add_tsum_inverse_natSuccSquare_of_memLp_two theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:226
BanditRLProof.tsum_sqrt_stoppingFiberRealMeasure_le_sqrt_integral_rounds_sq_mul_sqrt_tsum_inverse_natSuccSquare_of_memLp_two theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:336
BanditRLProof.integrable_stoppedValue_of_uniform_secondMoment_of_memLp_two_rounds theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:437
BanditRLProof.integral_abs_stoppedValue_le_uniformSecondMoment_mul_tsum_sqrt_stoppingFiberRealMeasure_of_memLp_two_rounds theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:554
BanditRLProof.integral_abs_stoppedValue_le_uniformSecondMoment_mul_sqrt_integral_rounds_sq_mul_sqrt_tsum_inverse_natSuccSquare_of_memLp_two_rounds theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:670
BanditRLProof.integral_abs_stoppedValue_le_uniformSecondMoment_mul_half_roundSecondMoment_add_inverseSquareTsum_of_memLp_two_rounds theorem Probability layer BanditRLProof.UnboundedStoppingTimeL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeL2CoordinateIntegrability.lean:717
BanditRLProof.measurable_stoppedValue_of_measurable_coordinates theorem Probability layer BanditRLProof.UnboundedStoppingTimeWeightedL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeWeightedL2CoordinateIntegrability.lean:24
BanditRLProof.summable_abs_weight_mul_sqrt_stoppingFiberRealMeasure_and_tsum_le theorem Probability layer BanditRLProof.UnboundedStoppingTimeWeightedL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeWeightedL2CoordinateIntegrability.lean:53
BanditRLProof.integrable_and_integral_abs_stoppedValue_weight_mul_le theorem Probability layer BanditRLProof.UnboundedStoppingTimeWeightedL2CoordinateIntegrability Compiled BanditRLProof/UnboundedStoppingTimeWeightedL2CoordinateIntegrability.lean:130