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chewi22a@v178@PMLR

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#1 Analysis of Langevin Monte Carlo from Poincare to Log-Sobolev [PDF2] [Copy] [Kimi2] [REL]

Authors: Sinho Chewi, Murat A Erdogdu, Mufan Li, Ruoqi Shen, Shunshi Zhang

Classically, the continuous-time Langevin diffusion converges exponentially fast to its stationary distribution π under the sole assumption that π satisfies a Poincaré inequality. Using this fact to provide guarantees for the discrete-time Langevin Monte Carlo (LMC) algorithm, however, is considerably more challenging due to the need for working with chi-squared or Rényi divergences, and prior works have largely focused on strongly log-concave targets. In this work, we provide the first convergence guarantees for LMC assuming that π satisfies either a LataÅ‚{}a–Oleszkiewicz or modified log-Sobolev inequality, which interpolates between the Poincaré and log-Sobolev settings. Unlike prior works, our results allow for weak smoothness and do not require convexity or dissipativity conditions.

Subject: COLT.2022 - Accept