D. Kuhn

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of probability distributions centered at the uniform distribution on the training samples, and we seek decisions that perform best in view of the worst-case distribution within this ball. We show that the resulting optimization problems can be solved efficiently and that their solutions enjoy powerful out-of-sample performance guarantees on test data. The wide applicability of this approach is illustrated with examples in portfolio selection, uncertainty quantification, statistical learning and inverse optimization.

Keywords: Robust optimization Wasserstein Metric