Overfitting in adversarially robust deep learning

It is common practice in deep learning to use overparameterized networks and train for as long as possible; there are numerous studies that show, both theoretically and empirically, that such practices surprisingly do not unduly harm the generalization performance of the classifier. In this paper, we empirically study this phenomenon in the setting of adversarially trained deep networks, which are trained to minimize the loss under worst-case adversarial perturbations. We find that overfitting to the training set does in fact harm robust performance to a very large degree in adversarially robust training across multiple datasets (SVHN, CIFAR-10, CIFAR-100, and ImageNet) and perturbation models ($\ell_\infty$ and $\ell_2$). Based upon this observed effect, we show that the performance gains of virtually all recent algorithmic improvements upon adversarial training can be matched by simply using early stopping. We also show that effects such as the double descent curve do still occur in adversarially trained models, yet fail to explain the observed overfitting. Finally, we study several classical and modern deep learning remedies for overfitting, including regularization and data augmentation, and find that no approach in isolation improves significantly upon the gains achieved by early stopping. All code for reproducing the experiments as well as pretrained model weights and training logs can be found at https://github.com/locuslab/robust_overfitting.

Fast is better than free: Revisiting adversarial training

Adversarial training, a method for learning robust deep networks, is typically assumed to be more expensive than traditional training due to the necessity of constructing adversarial examples via a first-order method like projected gradient decent (PGD). In this paper, we make the surprising discovery that it is possible to train empirically robust models using a much weaker and cheaper adversary, an approach that was previously believed to be ineffective, rendering the method no more costly than standard training in practice. Specifically, we show that adversarial training with the fast gradient sign method (FGSM), when combined with random initialization, is as effective as PGD-based training but has significantly lower cost. Furthermore we show that FGSM adversarial training can be further accelerated by using standard techniques for efficient training of deep networks, allowing us to learn a robust CIFAR10 classifier with 45% robust accuracy to PGD attacks with $\epsilon=8/255$ in 6 minutes, and a robust ImageNet classifier with 43% robust accuracy at $\epsilon=2/255$ in 12 hours, in comparison to past work based on "free" adversarial training which took 10 and 50 hours to reach the same respective thresholds. Finally, we identify a failure mode referred to as "catastrophic overfitting" which may have caused previous attempts to use FGSM adversarial training to fail. All code for reproducing the experiments in this paper as well as pretrained model weights are at https://github.com/locuslab/fast_adversarial.