Thompson Sampling for Bandits with Clustered Arms

TL;DR

This paper introduces multi-level Thompson sampling algorithms for clustered bandit problems, demonstrating improved regret bounds and computational efficiency by leveraging cluster structures, validated through theoretical analysis and empirical experiments.

Contribution

It presents novel algorithms that exploit cluster structures in bandit problems, providing theoretical regret bounds and empirical evidence of improved performance over existing methods.

Findings

Significant regret reduction when exploiting cluster structure

Improved computational efficiency over standard Thompson sampling

Empirical results outperform previous algorithms for clustered bandits

Abstract

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.