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.

33 pages

References in corpus (5)

• Canonical sampling through velocity-rescaling
• Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances
• Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlo
• Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models
• Couplings for Andersen Dynamics

Cited by in corpus (2)

• Piecewise deterministic sampling with splitting schemes
• Ballistic Convergence in Hit-and-Run Monte Carlo and a Coordinate-free Randomized Kaczmarz Algorithm