关于光滑性和等周性下Metropolis-Adjusted Langevin算法混合的简单证明

Apr, 2023

A Simple Proof of the Mixing of Metropolis-Adjusted Langevin Algorithm under Smoothness and Isoperimetry

Yuansi Chen, Khashayar Gatmiry

TL;DR本研究研究了在 $\mathbb{R}^d$ 上采样目标密度的 Metropolis-Adjusted Langevin 算法的混合时间，发现它在一定条件下的混合时间为 $O((L\Upsilon)^{\frac12}/\psi_\mu^2\log(1/\epsilon))$。

Abstract

We study the mixing time of metropolis-adjusted langevin algorithm (MALA) for sampling a target density on $\mathbb{R}^d$. We assume that