(More) Efficient Reinforcement Learning via Posterior Sampling

TL;DR

This paper explores posterior sampling for reinforcement learning (PSRL), an alternative to optimism-based algorithms, demonstrating its theoretical efficiency and practical superiority through regret bounds and simulations.

Contribution

It introduces PSRL, a simple, computationally efficient algorithm with near-optimal regret bounds, and shows its advantages over existing methods.

Findings

PSRL achieves an $ ilde{O}( au S oot{2} {A T})$ regret bound.

PSRL outperforms existing algorithms in simulations.

The approach naturally encodes prior knowledge.

Abstract

Most provably-efficient learning algorithms introduce optimism about poorly-understood states and actions to encourage exploration. We study an alternative approach for efficient exploration, posterior sampling for reinforcement learning (PSRL). This algorithm proceeds in repeated episodes of known duration. At the start of each episode, PSRL updates a prior distribution over Markov decision processes and takes one sample from this posterior. PSRL then follows the policy that is optimal for this sample during the episode. The algorithm is conceptually simple, computationally efficient and allows an agent to encode prior knowledge in a natural way. We establish an $\tilde{O}(\tau S \sqrt{AT})$ bound on the expected regret, where $T$ is time, $\tau$ is the episode length and $S$ and $A$ are the cardinalities of the state and action spaces. This bound is one of the first for an algorithm not based on optimism, and close to the state of the art for any reinforcement learning algorithm. We show through simulation that PSRL significantly outperforms existing algorithms with similar regret bounds.