Quantile Bandits for Best Arms Identification
This work addresses risk-averse decision-making in bandit problems, but it is incremental as it adapts an existing method to a quantile-based variant.
The paper tackles the problem of identifying the best arms in stochastic multi-armed bandits based on quantile values, motivated by risk-averse decision-making, and provides an algorithm with a theoretical upper bound on misidentification probability.
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 $τ$-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.