Quantile Bandits for Best Arms Identification with Concentration Inequalities

We consider a variant of the best arm identification task in stochastic multi-armed bandits. Motivated by risk-averse decision-making problems in fields like medicine, biology and finance, our goal is to identify a set of $m$ arms with the highest $\tau$-quantile values under a fixed budget. We propose Quantile Successive Accepts and Rejects algorithm (Q-SAR), the first quantile based algorithm for fixed budget multiple arms identification. We prove two-sided asymmetric concentration inequalities for order statistics and quantiles of random variables that have non-decreasing hazard rate, which may be of independent interest. With the proposed concentration inequalities, we upper bound the probability of arm misidentification for the bandit task. We show illustrative experiments for best arm identification.