Pure Exploration for Max-Quantile Bandits

We consider a variant of the pure exploration problem in Multi-Armed Bandits, where the goal is to find the arm for which the $$\lambda $$-quantile is maximal. Within the PAC framework, we provide a lower bound on the sample complexity of any $$\epsilon ,\delta $$-correct algorithm, and propose algorithms with matching upper bounds. Our bounds sharpen existing ones by explicitly incorporating the quantile factor $$\lambda $$. We further provide experiments that compare the sample complexity of our algorithms with that of previous works.