Harnessing the Power of Reinforcement Learning for Adaptive MCMC

Abstract: Sampling algorithms drive probabilistic machine learning, and recent years have seen an explosion in the diversity of tools for this task. However, the increasing sophistication of sampling algorithms is correlated with an increase in the tuning burden. There is now a greater need than ever to treat the tuning of samplers as a learning task in its own right. In a conceptual breakthrough, Wang et al (2025) formulated Metropolis-Hastings as a Markov decision process, opening up the possibility for adaptive tuning using Reinforcement Learning (RL). Their emphasis was on theoretical foundations; realising the practical benefit of Reinforcement Learning Metropolis-Hastings (RLMH) was left for subsequent work. The purpose of this paper is twofold: First, we observe the surprising result that natural choices of reward, such as the acceptance rate, or the expected squared jump distance, provide insufficient signal for training RLMH. Instead, we propose a novel reward based on the contrastive divergence, whose superior performance in the context of RLMH is demonstrated. Second, we explore the potential of RLMH and present adaptive gradient-based samplers that balance flexibility of the Markov transition kernel with learnability of the associated RL task. A comprehensive simulation study using the posteriordb benchmark supports the practical effectiveness of RLMH.