Efficient Learning for Selecting Top-m Context-Dependent Designs

TL;DR

This paper introduces an efficient Bayesian sequential sampling policy for selecting the top-m designs across different contexts in simulation optimization, achieving asymptotic optimality and improved efficiency.

Contribution

It formulates the problem as a stochastic dynamic programming task and derives asymptotically optimal sampling ratios for context-dependent design selection.

Findings

The proposed policy is proven to be consistent.

Asymptotic sampling ratios are asymptotically optimal.

Numerical experiments show improved efficiency in selecting top-m designs.

Abstract

We consider a simulation optimization problem for a context-dependent decision-making, which aims to determine the top-m designs for all contexts. Under a Bayesian framework, we formulate the optimal dynamic sampling decision as a stochastic dynamic programming problem, and develop a sequential sampling policy to efficiently learn the performance of each design under each context. The asymptotically optimal sampling ratios are derived to attain the optimal large deviations rate of the worst-case of probability of false selection. The proposed sampling policy is proved to be consistent and its asymptotic sampling ratios are asymptotically optimal. Numerical experiments demonstrate that the proposed method improves the efficiency for selection of top-m context-dependent designs.