Uncertainty Quantification and Exploration for Reinforcement Learning

TL;DR

This paper develops statistical tools for quantifying uncertainty in reinforcement learning, deriving asymptotic distributions of Q-values, and introduces a new exploration strategy that outperforms benchmarks in experiments.

Contribution

It provides the first explicit asymptotic variance formulas for Q-values in RL and proposes a novel exploration policy based on these statistical insights.

Findings

Derived closed-form asymptotic variances for Q-values.

Constructed valid confidence regions for RL quantities.

Proposed Q-OCBA exploration policy outperforms benchmarks.

Abstract

We investigate statistical uncertainty quantification for reinforcement learning (RL) and its implications in exploration policy. Despite ever-growing literature on RL applications, fundamental questions about inference and error quantification, such as large-sample behaviors, appear to remain quite open. In this paper, we fill in the literature gap by studying the central limit theorem behaviors of estimated Q-values and value functions under various RL settings. In particular, we explicitly identify closed-form expressions of the asymptotic variances, which allow us to efficiently construct asymptotically valid confidence regions for key RL quantities. Furthermore, we utilize these asymptotic expressions to design an effective exploration strategy, which we call Q-value-based Optimal Computing Budget Allocation (Q-OCBA). The policy relies on maximizing the relative discrepancies among the Q-value estimates. Numerical experiments show superior performances of our exploration strategy than other benchmark policies.