Why is Posterior Sampling Better than Optimism for Reinforcement Learning?

TL;DR

This paper demonstrates that posterior sampling for reinforcement learning (PSRL) significantly outperforms optimism-based algorithms like UCRL2, providing new theoretical regret bounds and insights into its superior performance.

Contribution

The paper offers a theoretical analysis explaining why PSRL outperforms optimism-based methods and establishes a tighter Bayesian regret bound of O(H\u221A(SAT)) in finite-horizon MDPs.

Findings

PSRL dramatically outperforms optimism-driven algorithms in practice.

A new Bayesian regret bound of O(HSST) is established.

Insight into the mechanisms driving PSRL's superior performance.

Abstract

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.