Reinforcement Learning for Adaptive MCMC
This work addresses the challenge of improving sampling efficiency in Bayesian inference, particularly for gradient-free methods, representing a novel integration of reinforcement learning into MCMC.
The paper tackles the problem of designing fast-mixing Markov transition kernels for adaptive MCMC by proposing a reinforcement learning framework called Reinforcement Learning Metropolis--Hastings, which outperforms a popular gradient-free adaptive Metropolis--Hastings algorithm on approximately 90% of tasks in the PosteriorDB benchmark.
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.