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.
Funding Statement
The work of N. Bou-Rabee has been partially supported by the National Science Foundation under Grant No. DMS-2111224. The work of S. Oberdörster has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
Acknowledgments
The authors are greatly indebted to Andreas Eberle for his guidance & support. They further thank the referees for their comments.
Citation
Nawaf Bou-Rabee. Stefan Oberdörster. "Mixing of Metropolis-adjusted Markov chains via couplings: The high acceptance regime." Electron. J. Probab. 29 1 - 27, 2024. https://doi.org/10.1214/24-EJP1150
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