Quantile Bandits for Best Arms Identification

Code

• github.com/Mengyanz/QSAR
  OfficialIn papernone★ 1
• github.com/Mengyanz/Mengyanz.github.io
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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 -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.

Tasks

Reproductions