WAT: Improve the Worst-class Robustness in Adversarial Training

Deep Neural Networks (DNN) have been shown to be vulnerable to adversarial examples. Adversarial training (AT) is a popular and effective strategy to defend against adversarial attacks. Recent works (Benz et al., 2020; Xu et al., 2021; Tian et al., 2021) have shown that a robust model well-trained by AT exhibits a remarkable robustness disparity among classes, and propose various methods to obtain consistent robust accuracy across classes. Unfortunately, these methods sacrifice a good deal of the average robust accuracy. Accordingly, this paper proposes a novel framework of worst-class adversarial training and leverages no-regret dynamics to solve this problem. Our goal is to obtain a classifier with great performance on worst-class and sacrifice just a little average robust accuracy at the same time. We then rigorously analyze the theoretical properties of our proposed algorithm, and the generalization error bound in terms of the worst-class robust risk. Furthermore, we propose a measurement to evaluate the proposed method in terms of both the average and worst-class accuracies. Experiments on various datasets and networks show that our proposed method outperforms the state-of-the-art approaches.