Reinforcement Learning for Adaptive MCMC

• URL: http://arxiv.org/abs/2405.13574v1
• Date: Wed, 22 May 2024 12:11:12 GMT
• Title: Reinforcement Learning for Adaptive MCMC
• Authors: Congye Wang, Wilson Chen, Heishiro Kanagawa, Chris. J. Oates,
• Abstract summary: The aim of this paper is to set out a general framework, called Reinforcement Learning Metropolis--Hastings. 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.
• Score: 6.773499165024668
• License: http://creativecommons.org/licenses/by/4.0/
• 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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