Quadratic Upper Bound for Boosting Robustness

Fast adversarial training (FAT) aims to enhance the robustness of models against adversarial attacks with reduced training time, however, FAT often suffers from compromised robustness due to insufficient exploration of adversarial space. In this paper, we develop a loss function to improve robustness in FAT without requiring stronger inner maximization. Specifically, we derive a quadratic upper bound (QUB) on the adversarial training (AT) loss function and propose to utilize the bound with existing FAT methods. Our experimental results show that applying QUB loss to the existing methods yields significant improvement of robustness. Furthermore, using various metrics, we demonstrate that this improvement is likely to result from the smoothened loss landscape of the resulting models.