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

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.