Generalizing Hierarchical Bayesian Bandits

A contextual bandit is a popular and practical framework for online learning to act under uncertainty. In many problems, the number of actions is huge and their mean rewards are correlated. In this work, we introduce a general framework for capturing such correlations through a two-level graphical model where actions are related through multiple shared latent parameters. We propose a Thompson sampling algorithm G-HierTS that uses this structure to explore efficiently and bound its Bayes regret. The regret has two terms, one for learning action parameters and the other for learning the shared latent parameters. The terms reflect the structure of our model as well as the quality of priors. Our theoretical findings are validated empirically using both synthetic and real-world problems. We also experiment with G-HierTS that maintains a factored posterior over latent parameters. While this approximation does not come with guarantees, it improves computational efficiency with a minimal impact on empirical regret.