AISTATS 2018poster0 citations
Stochastic Multi-armed Bandits in Constant Space
David Liau, Zhao Song, Eric Price, Ger Yang
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 $\sum_{i=1}^{K}\frac{1}{\Delta_i}\log \frac{\Delta_i}{∆}\log T$ where $\Delta_i$ is the gap between the best arm and arm $i$ and $∆$ 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 $O(\log (1/∆))$ factor of the optimum regret possible without space constraints.
BibTeX
@InProceedings{pmlr-v84-liau18a,
title = {Stochastic Multi-armed Bandits in Constant Space},
author = {Liau, David and Song, Zhao and Price, Eric and Yang, Ger},
booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics},
pages = {386--394},
year = {2018},
editor = {Storkey, Amos and Perez-Cruz, Fernando},
volume = {84},
series = {Proceedings of Machine Learning Research},
month = {09--11 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v84/liau18a/liau18a.pdf},
url = {https://proceedings.mlr.press/v84/liau18a.html},
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 $\sum_{i=1}^{K}\frac{1}{\Delta_i}\log \frac{\Delta_i}{∆}\log T$ where $\Delta_i$ is the gap between the best arm and arm $i$ and $∆$ 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 $O(\log (1/∆))$ factor of the optimum regret possible without space constraints.}
}