Quantile Bandits for Best Arms Identification
Abstract
We consider a variant of the best arm identification task in stochastic multi-armed bandits. Motivated by risk-averse decision-making problems, our goal is to identify a set of $m$ arms with the highest $\tau$-quantile values within a fixed budget. We prove asymmetric two-sided concentration inequalities for order statistics and quantiles of random variables that have non-decreasing hazard rate, which may be of independent interest. With these inequalities, we analyse a quantile version of Successive Accepts and Rejects (Q-SAR). We derive an upper bound for the probability of arm misidentification, the first justification of a quantile based algorithm for fixed budget multiple best arms identification. We show illustrative experiments for best arm identification.
BibTeX
@InProceedings{pmlr-v139-zhang21o,
title = {Quantile Bandits for Best Arms Identification},
author = {Zhang, Mengyan and Ong, Cheng Soon},
booktitle = {Proceedings of the 38th International Conference on Machine Learning},
pages = {12513--12523},
year = {2021},
editor = {Meila, Marina and Zhang, Tong},
volume = {139},
series = {Proceedings of Machine Learning Research},
month = {18--24 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v139/zhang21o/zhang21o.pdf},
url = {https://proceedings.mlr.press/v139/zhang21o.html},
abstract = {We consider a variant of the best arm identification task in stochastic multi-armed bandits. Motivated by risk-averse decision-making problems, our goal is to identify a set of $m$ arms with the highest $\tau$-quantile values within a fixed budget. We prove asymmetric two-sided concentration inequalities for order statistics and quantiles of random variables that have non-decreasing hazard rate, which may be of independent interest. With these inequalities, we analyse a quantile version of Successive Accepts and Rejects (Q-SAR). We derive an upper bound for the probability of arm misidentification, the first justification of a quantile based algorithm for fixed budget multiple best arms identification. We show illustrative experiments for best arm identification.}
}