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Adversarial training and data augmentation with noise are widely adoptedtechniques to enhance the performance of neural networks. This paperinvestigates adversarial training and data augmentation with noise in thecontext of regularized regression in a reproducing kernel Hilbert space (RKHS).We establish the limiting formula for these techniques as the attack and noisesize, as well as the regularization parameter, tend to zero. Based on thislimiting formula, we analyze specific scenarios and demonstrate that, withoutappropriate regularization, these two methods may have larger generalizationerror and Lipschitz constant than standard kernel regression. However, byselecting the appropriate regularization parameter, these two methods canoutperform standard kernel regression and achieve smaller generalization errorand Lipschitz constant. These findings support the empirical observations thatadversarial training can lead to overfitting, and appropriate regularizationmethods, such as early stopping, can alleviate this issue.

Understanding Overfitting in Adversarial Training via Kernel Regression