Why is Posterior Sampling Better than Optimism for Reinforcement Learning?

Computational results demonstrate that posterior sampling for reinforcement learning (PSRL) dramatically outperforms existing algorithms driven by optimism, such as UCRL2. We provide insight into the extent of this performance boost and the phenomenon that drives it. We leverage this insight to establish an $\tilde{O}(H\sqrt{SAT})$ Bayesian regret bound for PSRL in finite-horizon episodic Markov decision processes. This improves upon the best previous Bayesian regret bound of $\tilde{O}(H S \sqrt{AT})$ for any reinforcement learning algorithm. Our theoretical results are supported by extensive empirical evaluation.