Ensemble sampling for linear bandits: small ensembles suffice

David Janz; Alexander E. Litvak; Csaba Szepesvári

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arXiv · 2311.08376

Ensemble sampling for linear bandits: small ensembles suffice

David Janz·Alexander E. Litvak·Csaba Szepesvári

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Abstract

We provide the first useful and rigorous analysis of ensemble sampling for the stochastic linear bandit setting. In particular, we show that, under standard assumptions, for a $d$-dimensional stochastic linear bandit with an interaction horizon $T$, ensemble sampling with an ensemble of size of order $d \log T$ incurs regret at most of the order $(d \log T)^{5/2} \sqrt{T}$. Ours is the first result in any structured setting not to require the size of the ensemble to scale linearly with $T$ -- which defeats the purpose of ensemble sampling -- while obtaining near $\smash{\sqrt{T}}$ order regret. Our result is also the first to allow for infinite action sets.

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David Janz, Alexander E. Litvak, Csaba Szepesvári. 2023-11-14. Ensemble sampling for linear bandits: small ensembles suffice. https://arxiv.org/abs/2311.08376

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