An Information-Theoretic Analysis of Thompson Sampling

TL;DR

This paper offers an information-theoretic framework for analyzing Thompson sampling, providing regret bounds related to the entropy of the optimal actions, thereby enhancing understanding of how information influences learning efficiency.

Contribution

It introduces a broad, elegant analysis of Thompson sampling using information theory, strengthening existing regret bounds and offering new insights into information's role in learning.

Findings

Regret bounds scale with the entropy of the optimal-action distribution

Analysis applies across various online optimization problems

Provides new insights into information's impact on performance

Abstract

We provide an information-theoretic analysis of Thompson sampling that applies across a broad range of online optimization problems in which a decision-maker must learn from partial feedback. This analysis inherits the simplicity and elegance of information theory and leads to regret bounds that scale with the entropy of the optimal-action distribution. This strengthens preexisting results and yields new insight into how information improves performance.