Stochastic Multi-armed Bandits in Constant Space

Abstract

We consider the stochastic bandit problem in the sublinear space setting, where one cannot record the win-loss record for all $K$ arms. We give an algorithm using $O(1)$ words of space with regret \[ \sum_{i=1}^{K}\frac{1}{Δ_i}\log \frac{Δ_i}Δ\log T \] where $\hat{I}{”}_i$ is the gap between the best arm and arm $i$ and $\hat{I}”$ is the gap between the best and the second-best arms. If the rewards are bounded away from $0$ and $1$, this is within an $O(\log 1/\hat{I}”)$ factor of the optimum regret possible without space constraints.

AISTATS 2018