  Adversarial robustness has become an important research topic given empirical
demonstrations on the lack of robustness of deep neural networks.
Unfortunately, recent theoretical results suggest that adversarial training
induces a strict tradeoff between classification accuracy and adversarial
robustness. In this paper, we propose and then study a new regularization for
any margin classifier or deep neural network. We motivate this regularization
by a novel generalization bound that shows a tradeoff in classifier accuracy
between maximizing its margin and average margin. We thus call our approach an
average margin (AM) regularization, and it consists of a linear term added to
the objective. We theoretically show that for certain distributions AM
regularization can both improve classifier accuracy and robustness to
adversarial attacks. We conclude by using both synthetic and real data to
empirically show that AM regularization can strictly improve both accuracy and
robustness for support vector machine's (SVM's), relative to unregularized
classifiers and adversarially trained classifiers.
