Samplinglib
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upper · Normalized SampleWiki statement

Nonsmooth mirror-Langevin

A paper-first mathematical case study: read the theorem, the derivation route, and the hidden prerequisites before opening formal infrastructure.

Formal topologyOpen this result's proof branch↗
Statement

Normalized SampleWiki statement

Primary theorem audit pending — this is not presented as a verbatim paper theorem

Chewi (2026), Theorem 10.3.28primary theorem audit in progress
Guarantee / accuracy
\[\sqrt{\operatorname{KL}}\le\varepsilon\]
Complexity / rate
\[O(L^2D_\phi(\pi,\mu_{0+})/\varepsilon^4)\]

Reading. Read the accuracy guarantee together with the complexity/rate: the source assumptions and its notion of oracle cost are part of the result.

Primary theorem audit pending. The formulas below are the cleaned SampleWiki normalization of the cited result, not a claim of verbatim theorem transcription.

Proof / derivation

Reader derivation map · Mirror geometry and averaging route

This is a source-linked reading map for Chewi (2026), Theorem 10.3.28, not a transcription of the paper's proof. Exact source proof equations replace this map once theorem-level audit is complete.

01

Write the sampling dynamics in the source Bregman/mirror geometry rather than silently reverting to Euclidean distance.

02

Establish the corresponding descent/evolution inequality and isolate the discretization term.

03

Telescope or average the inequality in the geometry used by the theorem.

\[\sqrt{\operatorname{KL}}\le\varepsilon\]
04

Tune the step size to convert the geometric bound into the displayed KL/query complexity.

\[O(L^2D_\phi(\pi,\mu_{0+})/\varepsilon^4)\]
Assumptions and implicit prerequisites

What must be true before the rate can be read

Model and geometry

  • The potential is convex and satisfies the weak/Hölder smoothness model of the cited theorem.
  • The Hölder exponent and constant are source parameters; ASTIS does not silently replace them by ordinary smoothness.
  • The initial transport scale and the requested KL accuracy are kept explicit in the rate.

Analytic / proof prerequisites

  • Exact theorem-level parameter ranges and technical hypotheses remain controlled by the cited paper until primary-source audit is complete.
ASTIS rigorous LaTeX
Guarantee / accuracy
\[\sqrt{\operatorname{KL}}\le\varepsilon\]
Complexity / rate
\[O(L^2D_\phi(\pi,\mu_{0+})/\varepsilon^4)\]
Lean formalization

This fold is intentionally quiet while the source statement, proof route, and assumptions are being completed case by case. A source-facing Lean theorem will appear here only after it compiles and its statement has been matched to the audited source.

References and provenance

SampleWiki setting

ASTIS-SW-SETTING-HOLDER-SMOOTH-LOG-CONCAVE-UPPER-NONSMOOTH-MIRROR-LANGEVIN · source snapshot ba44eaedc763f364