Reinforcement Learning for Adaptive MCMC

TL;DR

This paper introduces a reinforcement learning framework for adaptive MCMC, specifically optimizing Metropolis--Hastings kernels with policy gradients, resulting in a more efficient sampler validated on benchmark tasks.

Contribution

It presents a theoretically supported, empirically validated RL-based framework for adaptive MCMC, focusing on learning fast-mixing kernels via policy gradient methods.

Findings

Outperforms existing gradient-free adaptive MCMC on 90% of tasks

Provides a theoretically grounded approach ensuring ergodicity

Demonstrates practical effectiveness on benchmark problems

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.