Why is Posterior Sampling Better than Optimism for Reinforcement Learning?

Computational results demonstrate that posterior sampling for reinforcement learning (PSRL) dramatically outperforms 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 expected regret bound for PSRL in finite-horizon episodic Markov decision processes, where $H$ is the horizon, $S$ is the number of states, $A$ is the number of actions and $T$ is the time elapsed. This improves upon the best previous bound of $\tilde{O}(H S \sqrt{AT})$ for any reinforcement learning algorithm.