Thompson Sampling for Bandits with Clustered Arms
This work addresses efficiency challenges in bandit algorithms for scenarios with clustered arms, offering incremental improvements over existing clustered bandit methods.
The paper tackles the problem of improving regret and computational efficiency in stochastic multi-armed bandits with clustered arms by proposing multi-level Thompson sampling algorithms, showing theoretical and empirical gains over standard methods.
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.