Distributionally Robust Optimization for Input Model Uncertainty in Simulation-based Decision Making

Abstract

We consider a new approach to solve distributionally robust optimization formulations that address nonparametric input model uncertainty in simulation-based decision making problems. Our approach for the minimax formulations applies stochastic gradient descent to the outer minimization problem and efficiently estimates the gradient of the inner maximization problem through multi-level Monte Carlo randomization. Using theoretical results that shed light on why standard gradient estimators fail, we establish the optimal parametrization of the gradient estimators of our approach that trades off between computation time and statistical variance. We apply our approach to nonconvex portfolio choice modeling under cumulative prospect theory, where numerical experiments demonstrate the significant benefits of this approach over previous related work.