  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.
