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We study distributionally robust optimization (DRO) problems where theambiguity set is defined using the Wasserstein metric. We show that this classof DRO problems can be reformulated as semi-infinite programs. We give anexchange method to solve the reformulated problem for the general nonlinearmodel, and a central cutting-surface method for the convex case, assuming thatwe have a separation oracle. We used a distributionally robust generalizationof the logistic regression model to test our algorithm. Numerical experimentson the distributionally robust logistic regression models show that the numberof oracle calls are typically 20 ? 50 to achieve 5-digit precision. Thesolution found by the model is generally better in its ability to predict witha smaller standard error.

Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric