title: I-PGD-AT: Efficient Adversarial Training via Imitating Iterative PGD Attack 
abstract: Adversarial training has been widely used in various machine learning paradigms to improve the robustness; while it would increase the training cost due to the perturbation optimization process. To improve the efficiency, recent studies leverage Fast Gradient Sign Method with Random Start (FGSM-RS) for adversarial training. However, such methods would lead to relatively low robustness and catastrophic overfitting, which means the robustness against iterative attacks (e.g. Projected Gradient Descent (PGD)) would suddenly drop to 0%. Different approaches have been proposed to address this problem, while later studies show that catastrophic overfitting still remains. In this paper, motivated by the fact that expensive iterative adversarial training methods achieve high robustness without catastrophic overfitting, we aim to ask: Can we perform iterative adversarial training in an efficient way? To this end, we first analyze the difference of perturbation generated by FGSM-RS and PGD and find that PGD tends to craft diverse discrete values instead of $\pm 1$ in FGSM-RS. Based on this observation, we propose an efficient single-step adversarial training method I-PGD-AT by adopting I-PGD attack for training, in which I-PGD imitates PGD virtually. Unlike FGSM that crafts the perturbation directly using the sign of gradient, I-PGD imitates the perturbation of PGD based on the magnitude of gradient. Extensive empirical evaluations on CIFAR-10 and Tiny ImageNet demonstrate that our I-PGD-AT can improve the robustness compared with the baselines and significantly delay catastrophic overfitting. Moreover, we explore and discuss the factors that affect catastrophic overfitting. Finally, to demonstrate the generality of I-PGD-AT, we integrate it into PGD adversarial training and show that it can even further improve the robustness.
authors: Xiaosen Wang Bhavya Kailkhura Krishnaram Kenthapadi Bo Li
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