Tight Bayesian Ambiguity Sets for Robust MDPs

Abstract: Robustness is important for sequential decision making in a stochastic dynamic environment with uncertain probabilistic parameters. We address the problem of using robust MDPs (RMDPs) to compute policies with provable worst-case guarantees in reinforcement learning. The quality and robustness of an RMDP solution is determined by its ambiguity set. Existing methods construct ambiguity sets that lead to impractically conservative solutions. In this paper, we propose RSVF, which achieves less conservative solutions with the same worst-case guarantees by 1) leveraging a Bayesian prior, 2) optimizing the size and location of the ambiguity set, and, most importantly, 3) relaxing the requirement that the set is a confidence interval. Our theoretical analysis shows the safety of RSVF, and the empirical results demonstrate its practical promise.