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We provide the first useful, rigorous analysis of ensemble sampling for thestochastic linear bandit setting. In particular, we show that, under standardassumptions, for a $d$-dimensional stochastic linear bandit with an interactionhorizon $T$, ensemble sampling with an ensemble of size $m$ on the order of $d\log T$ incurs regret bounded by order $(d \log T)^{5/2} \sqrt{T}$. Ours is thefirst result in any structured setting not to require the size of the ensembleto scale linearly with $T$ -- which defeats the purpose of ensemble sampling --while obtaining near $\sqrt{T}$ order regret. Ours is also the first resultthat allows infinite action sets.

Ensemble sampling for linear bandits: small ensembles suffice