Adversarial training based on the minimax formulation is necessary for obtaining adversarial robustness of trained models. However, it is conservative or even pessimistic so that it sometimes hurts the natural generalization. In this paper, we raise a fundamental question---do we have to trade off natural generalization for adversarial robustness? We argue that adversarial training is to employ confident adversarial data for updating the current model. We propose a novel approach of friendly adversarial training (FAT): rather than employing most adversarial data maximizing the loss, we search for least adversarial (i.e., friendly adversarial) data minimizing the loss, among the adversarial data that are confidently misclassified. Our novel formulation is easy to implement by just stopping the most adversarial data searching algorithms such as PGD (projected gradient descent) early, which we call early-stopped PGD. Theoretically, FAT is justified by an upper bound of the adversarial risk. Empirically, early-stopped PGD allows us to answer the earlier question negatively---adversarial robustness can indeed be achieved without compromising the natural generalization.

本研究提出了友好对抗训练(FAT)的新方法，其中通过提前停止最严格的对抗数据搜索算法，即早停止的PGD，来最小化损失并利用自信的对抗数据更新当前模型，理论上可以通过对抗风险的上限来证明，实验证明不需要以自然泛化为代价也可以实现对抗强度。

不致死的攻击使对抗学习更强大