Title: Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric,
Abstract: We study distributionally robust optimization (DRO) problems where the
ambiguity set is defined using the Wasserstein metric. We show that this class
of DRO problems can be reformulated as semi-infinite programs. We give an
exchange method to solve the reformulated problem for the general nonlinear
model, and a central cutting-surface method for the convex case, assuming that
we have a separation oracle. We used a distributionally robust generalization
of the logistic regression model to test our algorithm. Numerical experiments
on the distributionally robust logistic regression models show that the number
of oracle calls are typically 20 ? 50 to achieve 5-digit precision. The
solution found by the model is generally better in its ability to predict with
a smaller standard error.