The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, overfitting is typically mitigated by adding regularization terms to the objective that penalize hypothesis complexity. In this paper we introduce new regularization techniques using ideas from distributionally robust optimization, and we give new probabilistic interpretations to existing techniques. Specifically, we propose to minimize the worst-case expected loss, where the worst case is taken over the ball of all (continuous or discrete) distributions that have a bounded transportation distance from the (discrete) empirical distribution. By choosing the radius of this ball judiciously, we can guarantee that the worst-case expected loss provides an upper confidence bound on the loss on test data, thus offering new generalization bounds. We prove that the resulting regularized learning problems are tractable and can be tractably kernelized for many popular loss functions. We validate our theoretical out-of-sample guarantees through simulated and empirical experiments.

本文提出了使用分布式鲁邦优化的思想来作为正则化技术以及对现有技术提供新的概率解释。通过选择半径，可以保证最坏情况下的预期损失提供了对测试数据的上限置信度，从而提供新的泛化界限。

质量传输正则化