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Activity Number: 319 - SLDS CSpeed 6
Type: Contributed
Date/Time: Wednesday, August 11, 2021 : 3:30 PM to 5:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #317742
Title: On the Algorithmic Stability of Adversarial Training
Author(s): Yue Xing* and Qifan Song and Guang Cheng
Companies: Purdue University and Purdue University and Purdue University
Keywords: Adversarial Robustness; Adversarial Training; Algorithmic Stability; Regression; Classification

The adversarial training is a popular tool to remedy the vulnerability of deep learning models against adversarial attacks, and there is rich theoretical literature on the training loss of adversarial training algorithms. In contrast, this paper studies the algorithmic stability of a generic adversarial training algorithm, which can further help to establish an upper bound for generalization error. By figuring out the stability upper bound and lower bound, we argue that the non-differentiability issue of adversarial training causes worse algorithmic stability than their natural counterparts. To tackle this problem, we propose a noise injection method. While the non-differentiability problem seriously affects the stability of adversarial training, injecting noise enables the training trajectory to avoid the occurrence of non-differentiability with dominating probability, hence enhancing the stability performance of adversarial training. Our analysis also studies the relation between the algorithm stability and numerical approximation error of adversarial attacks.

Authors who are presenting talks have a * after their name.

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