Efficient Sampling Policy for Selecting a Good Enough Subset

TL;DR

This paper introduces a Bayesian sequential sampling policy designed to efficiently select a sufficiently good subset from many options within a fixed simulation budget, using approximate dynamic programming.

Contribution

It formulates the subset selection as a stochastic control problem and proposes a novel value function approximation-based sampling policy.

Findings

The policy maximizes the probability of correct subset selection.

Numerical experiments show the policy's efficiency and effectiveness.

Asymptotic analysis supports the policy's theoretical properties.

Abstract

The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting a good 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.