BanditRLlib
Lean gate passed before this site build; local proof declarations are shown as compiled.Lean-verified build · exact declarations linked.

Unclosed leaves, with the reason visible

BanditRLwiki Frontier

A mathematical literature gap is not the same as a missing source audit or a local Lean proof gap. This page keeps all three boundaries explicit.

0literature-open cases
36named formalization leaves
1source-audit cases
13formalization-open cases

Literature-open cases

These are explicit negative findings from the scoped primary-source audit. A missing database entry is never enough to place a case here.

No explicitly audited open leaf is registered.

Source-audit queue

These cases have a strong closest result, but a compatible primary upper/lower theorem pair has not yet been frozen. They are not labeled literature-open.

contextual-finite-policy-exp4pWhich exact contextual lower theorem matches the displayed Exp4.P contract, and how should its policy class be represented in Lean?Source audit pending

The Exp4.P upper theorem is frozen; the lower-source audit and all local formalization remain pending.

Related named obligations

  • Exact lower source
  • expert measurability
  • mixture action law
  • high-probability terminal

Inspect upper, lower, assumptions, and Lean evidence →

Formalization frontier

The mathematics may already be known, but the exact paper theorem or its required semantic bridge is not compiled in BanditRLlib.

stochastic-finite-arm-minimaxCan the exact anytime MOSS source theorem be compiled on one generated bounded-reward trajectory?Partial local route

The local Gaussian lower terminal and fixed-horizon MOSS near-minimax theorem compile; the distinct anytime variant remains unformalized.

Named formalization leaves

  • MOSS-ANYTIME-GENERATED-UPPER
  • Index measurability
  • armwise confidence
  • pull-count summation
  • expected-regret terminal

Inspect upper, lower, assumptions, and Lean evidence →

stochastic-instance-dependent-klucbCan the compiled finite-mean Lemma 16.3 be lifted through d_inf and liminf to the exact KL-UCB leading constant?Partial local route

The generated conservative KL-UCB route and exact Chapter 16 Lemma 16.3 compile; the d_inf-to-liminf bridge and Theorem 16.2 also compile.

Named formalization leaves

  • CH16-THM-16-2
  • d_inf branch analysis
  • liminf terminal
  • sharp KL-UCB upper constant

Inspect upper, lower, assumptions, and Lean evidence →

adversarial-exp3Can the local adversarial upper route be paired with a compiled minimax lower terminal under one exact regret contract?Partial local route

The EXP3 upper compiles; corrected Chapter 17 Theorem 17.4 now passes focused compilation with δ ≤ 1/32, c=1/160 and C=64; full local gates pass.

Named formalization leaves

  • CH17-CLIPPED-NORMAL-LAW
  • CH17-CLAIM-17-6
  • CH17-CLAIM-17-7
  • CH17-THM-17-4
  • matched upper/lower regret contract; corrected Chapter 17 high-probability construction is compiled

Inspect upper, lower, assumptions, and Lean evidence →

adversarial-stochastic-best-of-both-worldsCan one local generated half-Tsallis policy be shown identical to paper Tsallis-INF and carry both source guarantees?Partial local route

Several strong local endpoints compile, but they are not yet a unified source-identity theorem.

Named formalization leaves

  • TSALLIS-INF-PAPER-IDENTITY
  • TSALLIS-INF-SAME-POLICY-BOBW
  • Estimator identity
  • scheduler identity
  • same-policy paired theorem
  • constant audit

Inspect upper, lower, assumptions, and Lean evidence →

contextual-finite-policy-exp4pWhich exact contextual lower theorem matches the displayed Exp4.P contract, and how should its policy class be represented in Lean?Planned

The Exp4.P upper theorem is frozen; the lower-source audit and all local formalization remain pending.

Named formalization leaves

  • EXP4P-LOWER-SOURCE-AUDIT
  • EXP4P-CONTEXT-POLICY-INTERFACE
  • Exact lower source
  • expert measurability
  • mixture action law
  • high-probability terminal

Inspect upper, lower, assumptions, and Lean evidence →

stochastic-linear-ofulCan the finite-action scalar route be lifted to the exact OFUL theorem and paired with a compatible linear minimax lower construction?Partial local route

The local high-probability all-horizon consumer is strong but intentionally narrower than the source theorem.

Named formalization leaves

  • OFUL-SOURCE-THEOREM-13-IDENTITY
  • LINEAR-BANDIT-MINIMAX-LOWER
  • General decision set
  • source radius identity
  • hard family
  • upper/lower comparison terminal

Inspect upper, lower, assumptions, and Lean evidence →

finite-action-linear-contextualCan the exact Theorems 1–2 parameter fence and VCL construction be represented in one contextual Lean history law?Planned

The primary upper/lower comparison is audited; all local contextual algorithm and lower-construction work remains planned.

Named formalization leaves

  • VCL-CONTEXTUAL-HISTORY-LAW
  • VCL-LAYER-PARTITION
  • VCL-LOWER-CONSTRUCTION
  • Contextual history law
  • VCL layers
  • parameter fence
  • lower construction

Inspect upper, lower, assumptions, and Lean evidence →

tabular-finite-horizon-rl-ucbviCan the recurrent generated UCBVI source be upgraded from Hoeffding bonuses to the exact Bernstein/Freedman source theorem?Partial local route

The source-shaped UCBVI-CH endpoint compiles with the exact 20/250 surface; the minimax-leading UCBVI-BF route is absent.

Named formalization leaves

  • UCBVI-BF-CONDITIONAL-VARIANCE
  • UCBVI-BF-TOTAL-VARIANCE
  • UCBVI-BF-TERMINAL
  • Conditional variance
  • Freedman concentration
  • variance bonus summation
  • source-leading terminal

Inspect upper, lower, assumptions, and Lean evidence →

delayed-adversarial-banditCan the delayed accounting layer be connected to one generated algorithm law and a paper-level regret terminal?Partial local route

The bookkeeping, causal-view, active-allocation, and conditional source-audit surfaces compile; no algorithm regret theorem is claimed.

Named formalization leaves

  • DELAYED-TRAJECTORY-LAW
  • DELAYED-SAPO-D10-D12
  • DELAYED-REGRET-TERMINAL
  • Out-of-order reveal law
  • state machine
  • width audit
  • regret terminal

Inspect upper, lower, assumptions, and Lean evidence →

nonstationary-variation-budgetCan the current dynamic-regret envelope be specialized to the exact variation-budget Rexp3 theorem?Partial local route

A related drifting-mean theorem compiles, but its contract and rate are not the source minimax V_T result.

Named formalization leaves

  • VARIATION-BUDGET-DEFINITION
  • REXP3-BLOCK-RESTART
  • REXP3-DYNAMIC-REGRET
  • Variation measure
  • restart construction
  • oracle decomposition
  • rate optimization

Inspect upper, lower, assumptions, and Lean evidence →

nonstationary-best-arm-switch-budgetCan oracle global-mean restarts be replaced by an observed-reward detector under the broader best-arm-identity switch contract?Partial local route

The local theorem has the desired square-root expression only under a true global-change schedule; ArmSwitch is adaptive under a different, broader change count.

Named formalization leaves

  • BEST-ARM-SWITCH-CONTRACT
  • OBSERVED-CHANGE-DETECTOR
  • ADAPTIVE-RESTART-REGRET
  • Assumption bridge
  • detector measurability
  • false-alarm control
  • delay charge

Inspect upper, lower, assumptions, and Lean evidence →

fixed-confidence-best-arm-identificationHow should the characteristic-time max-min game and an unbounded adaptive stopping rule be represented in Lean?Planned

General stopping-time infrastructure exists elsewhere in BanditRLlib, but no pure-exploration semantic bridge or source theorem is mapped.

Named formalization leaves

  • BAI-DELTA-PAC
  • BAI-STOPPED-CHANGE-OF-MEASURE
  • BAI-CHARACTERISTIC-TIME
  • TRACK-AND-STOP
  • Recommendation event
  • stopping measurability
  • information game
  • tracking rule

Inspect upper, lower, assumptions, and Lean evidence →

distributional-high-probability-regretCan the compiled corrected lower terminal be paired with a formalized EQO+ upper route?Partial local route

Theorem 17.1, Corollaries 17.2–17.3, Eq. (17.8), corrected Claim 17.6, exact Claim 17.7, and corrected Theorem 17.4 pass the full local repository gate. Theorem 17.4 uses 0 < δ ≤ 1/32, c=1/160, C=64. No EQO+ algorithm theorem is claimed.

Named formalization leaves

  • CH17-HISTORY-INFORMATION
  • CH17-THEOREM-17-1
  • CH17-COROLLARY-17-2
  • CH17-COROLLARY-17-3
  • EQOPLUS-UPPER
  • EQO+ source map and formalized upper terminal

Inspect upper, lower, assumptions, and Lean evidence →

Active source ports outside the comparison atlas

These two NeurIPS 2025 ports record current compiled progress and exact nonclaims. One now contains a narrowly scoped compiled paper endpoint, while both remain partial audits and remain outside the minimax ledger until their remaining contracts and compatible comparison partners are frozen.

Source-frozen external audit

Succinct stochastic-bandit lower-bound geometry

Partial

A Novel General Framework for Sharp Lower Bounds in Succinct Stochastic Bandits

Guo Zeng and Jean Honorio · 2025

54 named declarations compile in the current library.

Definitions 3.1–3.3, Lemmas 3.1–3.4, the finite-Bessel strict-support route, and a global-R boundedness diagnostic compile.

Boundary. This is a source-frozen partial port, not yet an assumption-matched upper/lower comparison case. Lemmas 3.5–3.6, Assumption 3.7, Theorem 3.8, and every regret endpoint remain uncompiled.
Representative Lean declarations
Open official proceedings source ↗

Source-frozen external audit

Stochastic-gradient bandit Theorem 1, Corollary 1, and blocked Theorem-2 follow-on

Partial

Does Stochastic Gradient really succeed for Bandits?

Dorian Baudry, Emmeran Johnson, Simon Vary, Ciara Pike-Burke, and Patrick Rebeschini · 2025

361 named declarations compile in the current library.

The counted SGB audit retains the exact 361 = 223 + 23 + 25 + 26 + 7 + 8 + 13 + 28 + 8 audit-slice inventory through one-step selected-reward freshness, terminal-count events, nth-pull-to-count bridges, and a generic finite-horizon low-count regret consumer. A separate ten-declaration native-law module identifies the complete visible/native trajectory law. The selected-block module now has 36 declarations: eight transport finite optimal-arm pull-time/reward blocks to a masked latent-coupling law with explicit `WithTop Nat` missing pulls, fourteen define and transport the exact finite Appendix-C `S0/S1` event, ten split the pure latent phase probability into the generated all-present event plus an explicit missing-pull event, and four map the missing branch to a low-count event, transport its probability to the generated trajectory, and charge its existing mass against expected sampled pseudo-regret. The exact Theorem-1 and Corollary-1 endpoints use generated zero-initialized two-arm fixed-IID trajectories with a Unit Dirac environment prior; the reward laws themselves remain bounded fixed-IID laws. Corollary 1 assumes T >= 2, 0 < Delta < 1, and one fixed eta_T = sqrt(log T / T) per horizon.

Boundary. The audit remains partial. Corollary 1 is a direct Theorem-1 consumer, not evidence for the polynomial-regret Theorem 2. Complete visible/native law equality, missing-pull-aware selected-block transport, exact finite phase-event transport, the disjoint missing/all-present probability split, the missing-pull-to-terminal-count inclusion, and the missing-pull finite-horizon expected-regret consumer now compile. None is a selected-IID theorem or a positive-probability producer. The next unique leaf is the generated all-present Appendix-C phase trigger at a fixed chronological cutoff; the stopped-prefix future-cylinder law, conditional no-return probability >= 1/2, Rademacher/binomial ballot probability, asymptotic assembly, and the frozen terminal remain blocked. Theorem 4 likewise still lacks the general-K generated process, uniform buffer/survival producer, stopped supermartingale/Doob route, and final regret assembly.
Representative Lean declarations
Open official proceedings source ↗

How a leaf closes

  1. Freeze the contract.Fix assumptions, regret notion, quantifiers, constants, and source location.
  2. Audit primary evidence.Record the closest compatible upper and lower theorem; name every mismatch.
  3. Compile the exact bridge.Close one named proof obligation without adding an unadvertised assumption.
  4. Pass independent gates.Lean, tests, website links, source review, and deployment evidence must agree before status promotion.