Reinforcement Learning for Adaptive MCMC

Congye Wang; Wilson Chen; Heishiro Kanagawa; Chris. J. Oates

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arXiv · 2405.13574

Reinforcement Learning for Adaptive MCMC

Congye Wang·Wilson Chen·Heishiro Kanagawa·Chris. J. Oates

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Abstract

An informal observation, made by several authors, is that the adaptive design of a Markov transition kernel has the flavour of a reinforcement learning task. Yet, to-date it has remained unclear how to actually exploit modern reinforcement learning technologies for adaptive MCMC. The aim of this paper is to set out a general framework, called Reinforcement Learning Metropolis--Hastings, that is theoretically supported and empirically validated. Our principal focus is on learning fast-mixing Metropolis--Hastings transition kernels, which we cast as deterministic policies and optimise via a policy gradient. Control of the learning rate provably ensures conditions for ergodicity are satisfied. The methodology is used to construct a gradient-free sampler that out-performs a popular gradient-free adaptive Metropolis--Hastings algorithm on $\approx 90 \%$ of tasks in the PosteriorDB benchmark.

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BibTeX RIS

Congye Wang, Wilson Chen, Heishiro Kanagawa, Chris. J. Oates. 2024-05-22. Reinforcement Learning for Adaptive MCMC. https://arxiv.org/abs/2405.13574

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