  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.
