Why is Posterior Sampling Better than Optimism for Reinforcement Learning?
This provides a theoretical improvement for reinforcement learning algorithms in finite-horizon episodic Markov decision processes, though it appears incremental as it refines existing bounds.
The paper tackles the problem of reinforcement learning by showing that posterior sampling (PSRL) outperforms optimism-driven algorithms like UCRL2, establishing a Bayesian expected regret bound of $ ilde{O}(H\sqrt{SAT})$, which improves upon the previous best bound of $ ilde{O}(H S \sqrt{AT})$.
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.