Thompson Sampling for Bandits with Clustered Arms

Thompson Sampling for Bandits with Clustered Arms

Emil Carlsson, Devdatt Dubhashi, Fredrik D. Johansson

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence
Main Track. Pages 2212-2218. https://doi.org/10.24963/ijcai.2021/305

We propose algorithms based on a multi-level Thompson sampling scheme, for the stochastic multi-armed bandit and its contextual variant with linear expected rewards, in the setting where arms are clustered. We show, both theoretically and empirically, how exploiting a given cluster structure can significantly improve the regret and computational cost compared to using standard Thompson sampling. In the case of the stochastic multi-armed bandit we give upper bounds on the expected cumulative regret showing how it depends on the quality of the clustering. Finally, we perform an empirical evaluation showing that our algorithms perform well compared to previously proposed algorithms for bandits with clustered arms.
Keywords:
Machine Learning: Online Learning
Machine Learning: Learning Theory
Machine Learning: Reinforcement Learning