An Information-Theoretic Analysis of Thompson Sampling

Daniel Russo, Benjamin Van Roy

Published 2014-03-21, updated 2015-06-08Version 2

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.