Mixed-Effect Thompson Sampling

A contextual bandit is a popular framework for online learning to act under uncertainty. In practice, the number of actions is huge and their expected rewards are correlated. In this work, we introduce a general framework for capturing such correlations through a mixed-effect model where actions are related through multiple shared effect parameters. We propose Mixed-Effect Thompson Sampling (meTS) that uses this structure to explore efficiently and bound its Bayes regret. The regret bound has two terms, one for learning the action parameters and the other for learning the shared effect parameters. The terms reflect the structure of our model and the quality of priors. Our theoretical findings are validated empirically using both synthetic and real-world problems. We also propose numerous extensions of practical interest. While they do not come with guarantees, they perform extremely well empirically and show the generality of the proposed framework.