Part of Advances in Neural Information Processing Systems 37 (NeurIPS 2024) Main Conference Track
David Janz, Alexander Litvak, Csaba Szepesvari
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. Our result is also the first to allow for infinite action sets.