Efficient Dynamic Allocation Policy for Robust Ranking and Selection under Stochastic Control Framework

TL;DR

This paper introduces a Bayesian stochastic control approach for dynamic simulation budget allocation in ranking and selection problems, optimizing the probability of correctly identifying the best alternative under uncertainty.

Contribution

It develops a novel one-step-ahead dynamic optimal policy based on approximate dynamic programming, ensuring consistency and asymptotic optimality.

Findings

Significant performance improvements demonstrated in numerical experiments

Proposed policy outperforms existing static allocation methods

The approach effectively handles input uncertainty in ranking and selection

Abstract

This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured by its worst-case performance. We formulate the dynamic simulation budget allocation decision problem as a stochastic control problem under a Bayesian framework. Following the approximate dynamic programming theory, we derive a one-step-ahead dynamic optimal budget allocation policy and prove that this policy achieves consistency and asymptotic optimality. Numerical experiments demonstrate that the proposed procedure can significantly improve performance.