Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the training distribution is an exact upper bound on the true risk with high probability. However, existing guarantees either suffer from the curse of dimensionality, are restricted to specific settings, or lead to spurious error terms. In this paper, we show that these generalization guarantees actually hold on general classes of models, do not suffer from the curse of dimensionality, and can even cover distribution shifts at testing. We also prove that these results carry over to the newly-introduced regularized versions of Wasserstein distributionally robust problems.

翻译：Wasserstein分布鲁棒估计量已成为不确定性下预测与决策的强大模型。这类估计量提供了具有吸引力的泛化保证：由训练分布获得的鲁棒目标函数以高概率成为真实风险的确切上界。然而，现有保证要么受到维度灾难的限制，要么局限于特定场景，或导致虚假误差项。本文证明，这些泛化保证实际上在一般模型类别上成立，既不受维度灾难影响，甚至能涵盖测试时的分布偏移。我们还证明，这些结论可延伸至新近提出的正则化版本Wasserstein分布鲁棒问题。