Posterior Coreset Construction with Kernelized Stein Discrepancy for Model-Based Reinforcement Learning

Abstract

Model-based approaches to reinforcement learning (MBRL) exhibit favorable performance in practice, but their theoretical guarantees in large spaces are mostly restricted to the setting when transition model is Gaussian or Lipschitz, and demands a posterior estimate whose representational complexity grows unbounded with time. In this work, we develop a novel MBRL method (i) which relaxes the assumptions on the target transition model to belong to a generic family of mixture models; (ii) is applicable to large-scale training by incorporating a compression step such that the posterior estimate consists of a Bayesian coreset of only statistically significant past state-action pairs; and (iii) exhibits a sublinear Bayesian regret. To achieve these results, we adopt an approach based upon Stein's method, which, under a smoothness condition on the constructed posterior and target, allows distributional distance to be evaluated in closed form as the kernelized Stein discrepancy (KSD). The aforementioned compression step is then computed in terms of greedily retaining only those samples which are more than a certain KSD away from the previous model estimate. Experimentally, we observe that this approach is competitive with several state-of-the-art RL methodologies, and can achieve up-to 50 percent reduction in wall clock time in some continuous control environments.