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Despite remarkable success in practice, modern machine learning models havebeen found to be susceptible to adversarial attacks that makehuman-imperceptible perturbations to the data, but result in serious andpotentially dangerous prediction errors. To address this issue, practitionersoften use adversarial training to learn models that are robust against suchattacks at the cost of higher generalization error on unperturbed test sets.The conventional wisdom is that more training data should shrink the gapbetween the generalization error of adversarially-trained models and standardmodels. However, we study the training of robust classifiers for both Gaussianand Bernoulli models under $\ell_\infty$ attacks, and we prove that more datamay actually increase this gap. Furthermore, our theoretical results identifyif and when additional data will finally begin to shrink the gap. Lastly, weexperimentally demonstrate that our results also hold for linear regressionmodels, which may indicate that this phenomenon occurs more broadly.

More Data Can Expand the Generalization Gap Between Adversarially Robust and Standard Models