Quantile Bandits for Best Arms Identification

• URL: http://arxiv.org/abs/2010.11568v2
• Date: Fri, 11 Jun 2021 12:17:41 GMT
• Title: Quantile Bandits for Best Arms Identification
• Authors: Mengyan Zhang and Cheng Soon Ong
• Abstract summary: We consider a variant of the best arm identification task in 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.
• Score: 10.294977861990203
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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