Efficient Sampling Allocation Procedures for Optimal Quantile Selection

We propose a dynamic sampling allocation and selection paradigm for finding the alternative with the optimal quantile in a Bayesian framework. Myopic allocation policies (MAPs), analogous to existing methods in classic ranking and selection for selecting the alternative with the optimal mean, and computationally efficient selection policies are derived for selecting the alternative with the optimal quantile. Under certain conditions, we prove that the proposed MAPs and selection procedures are consistent, which means that the best quantile would be eventually correctly selected as the sample size goes to infinity. Numerical experiments demonstrate that the proposed schemes can significantly improve the performance.