Efficient Sampling Policy for Selecting a Subset With the Best

In this article, we study the problem of selecting a subset with the best of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting such a subset. We formulate the dynamic sampling decision as a stochastic control problem in a Bayesian setting. In an approximate dynamic programming paradigm, we propose a sequential sampling policy based on value function approximation. We analyze the asymptotic property of the proposed sampling policy. Numerical experiments demonstrate the efficiency of the proposed procedure.