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Oral
in
Workshop: 2nd ICML Workshop on New Frontiers in Adversarial Machine Learning

Adversarial Training with Generated Data in High-Dimensional Regression: An Asymptotic Study

Keywords: [ high-dimensional statistics ] [ Adversarial training ]


Abstract: In recent years, studies such as \cite{carmon2019unlabeled,gowal2021improving,xing2022artificial} have demonstrated that incorporating additional real or generated data with pseudo-labels can enhance adversarial training through a two-stage training approach. In this paper, we perform a theoretical analysis of the asymptotic behavior of this method in high-dimensional linear regression. While a double-descent phenomenon can be observed in ridgeless training, with an appropriate $\mathcal{L}_2$ regularization, the two-stage adversarial training achieves a better performance. Finally, we derive a shortcut cross-validation formula specifically tailored for the two-stage training method.

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