@inproceedings{
xie2024highdimensional,
title={High-dimensional (Group) Adversarial Training in Linear Regression},
author={Yiling Xie and Xiaoming Huo},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=Tsb4dVtCHx}
}
Adversarial training can achieve robustness against adversarial perturbations and has been widely used in machine-learning models. This paper delivers a non-asymptotic consistency analysis of the adversarial training procedure under $\ell_\infty$-perturbation in high-dimensional linear regression. It will be shown that, under the restricted eigenvalue condition, the associated convergence rate of prediction error can achieve the minimax rate up to a logarithmic factor in the high-dimensional linear regression on the class of sparse parameters. Additionally, the group adversarial training procedure is analyzed. Compared with classic adversarial training, it will be proved that the group adversarial training procedure enjoys a better prediction error upper bound under certain group-sparsity patterns.
High-dimensional (Group) Adversarial Training in Linear Regression
Yiling Xie Xiaoming Huo