Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees

TL;DR

This paper develops a robust, worst-case analysis framework for stochastic simulation that accounts for input model uncertainty, providing performance guarantees and a numerical scheme for optimization under these conditions.

Contribution

It introduces a novel approach combining worst-case analysis with a stochastic approximation method for robust simulation performance evaluation.

Findings

The proposed FWSA method converges on non-convex problems.

Numerical examples demonstrate the effectiveness of the approach.

The framework provides robustness guarantees for simulation analysis.

Abstract

Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use of worst-case analysis to analyze these errors, by representing the partial, nonparametric knowledge of the input models via optimization constraints. We study the performance and robustness guarantees of this approach. We design and analyze a numerical scheme for solving a general class of simulation objectives and uncertainty specifications. The key steps involve a randomized discretization of the probability spaces, a simulable unbiased gradient estimator using a nonparametric analog of the likelihood ratio method, and a Frank-Wolfe (FW) variant of the stochastic approximation (SA) method (which we call FWSA) run on the space of input probability distributions. A convergence analysis for FWSA on non-convex problems is provided. We test the performance of our approach via several numerical examples.