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arXiv · 1712.09007

Stochastic Multi-armed Bandits in Constant Space

David Liau·Eric Price·Zhao Song·Ger Yang
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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 \[ \sum_{i=1}^{K}\frac{1}{\Delta_i}\log \frac{\Delta_i}{\Delta}\log T \] where $\Delta_i$ is the gap between the best arm and arm $i$ and $\Delta$ 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 $O(\log 1/\Delta)$ factor of the optimum regret possible without space constraints.

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David Liau, Eric Price, Zhao Song, Ger Yang. 2017-12-25. Stochastic Multi-armed Bandits in Constant Space. https://arxiv.org/abs/1712.09007

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