Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees

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 a general class of simulation objectives and uncertainty specifications, based on a Frank-Wolfe (FW) variant of the stochastic approximation (SA) method (which we call FWSA) run on the space of input probability distributions. The key steps involve a randomized discretization of the probability spaces and the construction of simulable unbiased gradient estimators using a nonparametric analog of the classical likelihood ratio method. A convergence analysis for FWSA on non-convex problems is provided. We test the performance of our approach via several numerical examples.