Data-Driven Optimal Allocation for Ranking and Selection under Unknown Sampling Distributions

Ranking and selection (R&S) is the problem of identifying the optimal alternative from multiple alternatives through sampling them. In the existing R&S literature, sampling distributions of the observations are usually assumed to be from some known parametric distribution families, even in works that consider input uncertainty. By contrast, this paper considers R&S under completely unknown sampling distributions. We for the first time propose a data-driven nonparametric tuning-free sequential budget allocation strategy that can asymptotically achieve the optimal allocation specified by large deviation analysis. Especially, we propose a new point estimation approach for estimating the optimal large deviation rates directly, which efficiently solves the challenge of estimating large deviation rate functions for lack of known sampling distributions.