An Information-Theoretic Analysis of Thompson Sampling

Daniel Russo, Benjamin Van Roy.

Year: 2016, Volume: 17, Issue: 68, Pages: 1−30


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.