Data-Driven Sequential Sampling for Tail Risk Mitigation

Given a finite collection of stochastic alternatives, we study the problem of sequentially allocating a fixed sampling budget to identify the optimal alternative with a high probability, where the optimal alternative is defined as the one with the smallest value of extreme tail risk. We particularly consider a situation where these alternatives generate heavy-tailed losses whose probability distributions are unknown and may not admit any specific parametric representation. In this setup, we propose data-driven sequential sampling policies that maximize the rate at which the likelihood of falsely selecting suboptimal alternatives decays to zero. We rigorously demonstrate the superiority of the proposed methods over existing approaches, which is further validated via numerical studies.