Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime

TL;DR

This paper introduces a coupling framework to analyze the mixing times of Metropolis-adjusted Markov chains in high acceptance regimes, providing new guarantees especially for non-reversible chains like those based on kinetic Langevin diffusion.

Contribution

It develops a novel coupling approach to bound mixing times of gradient-based Metropolis kernels in high acceptance regimes, including for non-reversible chains.

Findings

Provides mixing time bounds for Metropolis-adjusted kernels in high acceptance regimes.

Extends analysis to non-reversible Markov chains based on kinetic Langevin diffusion.

Uses localization to connect local and global mixing properties.

Abstract

We present a coupling framework to upper bound the total variation mixing time of various Metropolis-adjusted, gradient-based Markov kernels in the `high acceptance regime'. The approach uses a localization argument to boost local mixing of the underlying unadjusted kernel to mixing of the adjusted kernel when the acceptance rate is suitably high. As an application, mixing time guarantees are developed for a non-reversible, adjusted Markov chain based on the kinetic Langevin diffusion, where little is currently understood.