Ensemble sampling for linear bandits: small ensembles suffice

• URL: http://arxiv.org/abs/2311.08376v3
• Date: Thu, 31 Oct 2024 15:42:51 GMT
• Title: Ensemble sampling for linear bandits: small ensembles suffice
• Authors: David Janz, Alexander E. Litvak, Csaba Szepesvári,
• Abstract summary: We provide the first useful and rigorous analysis of ensemble sampling for the linear bandit setting. Ours is the first result in any structured setting not to require the size of the ensemble to scale linearly with $T$ -- while obtaining near $smashsqrtT$ order regret.
• Score: 75.4286948336835
• License:
• 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 $\smash{d \log T}$ incurs regret at most of the order $\smash{(d \log T)^{5/2} \sqrt{T}}$. 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. Ours is also the first result that allows infinite action sets.

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