A nonparametric Bayesian approach for simulation optimization with input uncertainty

Abstract

Stochastic simulation models are increasingly popular for analyzing complex stochastic systems. However, the input distributions required to drive the simulation are typically unknown in practice and are usually estimated from real world data. Since the amount of real world data tends to be limited, the resulting estimation of the input distribution will contain errors. This estimation error is commonly known as input uncertainty. In this paper, we consider the stochastic simulation optimization problem when input uncertainty is present and assume that both the input distribution family and the distribution parameters are unknown. We adopt a nonparametric Bayesian approach to model the input uncertainty and propose a nonparametric Bayesian risk optimization (NBRO) framework to study simulation optimization under input distribution uncertainty. We establish the consistency and asymptotic normality of the value of the objective function, the optimal solution, and the optimal value for the NBRO problem. We further propose a simulation optimization algorithm based on Efficient Global Optimization (EGO), which explicitly takes into account the input uncertainty so as to efficiently solve the NBRO problem. We study the consistency property of the modified EGO algorithm and empirically test its efficiency with an inventory example and a critical care facility problem.