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Quantile Bandits for Best Arms Identification
Mengyan Zhang · Cheng Soon Ong

Wed Jul 21 09:00 PM -- 11:00 PM (PDT) @ None #None
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.

Author Information

Mengyan Zhang (The Australian National University; Data61, CSIRO)
Cheng Soon Ong (Data61 and ANU)

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