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条件下预测与决策的有力模型。这些估计量提供了极具吸引力的泛化保证：基于训练分布得到的鲁棒目标函数，能以高概率成为真实风险的上确界。然而，现有保证要么受维度灾难困扰，局限于特定场景，或产生虚假误差项。本文证明，这些泛化保证实际上适用于一般模型类别，不仅不受维度灾难影响，甚至能覆盖测试阶段的分布偏移。我们同时证明，这些结论可推广至新近提出的Wasserstein分布鲁棒问题的正则化版本。