Policy Certificates and Minimax-Optimal PAC Bounds for Episodic Reinforcement Learning

Designing reinforcement learning methods which find a good policy with as few samples as possible is a key goal of both empirical and theoretical research. On the theoretical side there are two main ways, regret- or PAC (probably approximately correct) bounds, to measure and guarantee sample-efficiency of a method. Ideally, we would like to have algorithms that have good performance according to both criteria, as they measure different aspects of sample efficiency and we have shown previously [1] that one cannot simply go from one to the other. In a specific setting called tabular episodic MDPs, a recent algorithm achieved close to optimal regret bounds [2] but there was no methods known to be close to optimal according to the PAC criterion despite a long line of research. In our work presented at ICML 2019, we close this gap with a new method that achieves minimax-optimal PAC (and regret) bounds which match the statistical worst-case lower bounds in the dominating terms.