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.

本文研究了基于 Wasserstein 距离的分布鲁棒优化问题，将其归约为半无限规划问题，并提供了求解非线性模型的交换算法和凸情况下基于分离预言的中心割面算法，通过对分布鲁棒广义 logistic 回归模型的数字实验表明，该算法无论是在预测精度上还是在标准误差方面都表现得更好。