Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of robust models based on the Wasserstein distance have generalization guarantees that do not suffer from the curse of dimensionality. However, these results are either approximate, obtained in specific cases, or based on assumptions difficult to verify in practice. In contrast, we establish exact generalization guarantees that cover a wide range of cases, with arbitrary transport costs and parametric loss functions, including deep learning objectives with nonsmooth activations. We complete our analysis with an excess bound on the robust objective and an extension to Wasserstein robust models with entropic regularizations.

翻译：分布鲁棒优化已成为训练鲁棒机器学习模型的一种有吸引力的方法，能够捕捉数据不确定性和分布偏移。最近的统计分析证明，基于Wasserstein距离的鲁棒模型具有不受维度诅咒影响的泛化保证。然而，这些结果要么是近似的，要么是在特定情况下获得的，要么基于在实践中难以验证的假设。相比之下，我们建立了精确的泛化保证，涵盖了广泛的情况，包括任意传输成本和参数化损失函数，其中包含具有非光滑激活函数的深度学习目标。我们通过鲁棒目标函数的超额界分析以及对具有熵正则化的Wasserstein鲁棒模型的扩展，完善了我们的理论分析。