More Data Can Expand the Generalization Gap Between Adversarially Robust and Standard Models
This finding challenges a key assumption in adversarial training, potentially impacting practitioners who rely on data scaling to improve robust model performance, though it is incremental as it builds on existing adversarial robustness research.
The paper tackles the problem of adversarial robustness in machine learning by showing that, contrary to conventional wisdom, more training data can increase the generalization gap between adversarially robust and standard models, with theoretical proofs for Gaussian and Bernoulli models and experimental validation for linear regression.
Despite remarkable success in practice, modern machine learning models have been found to be susceptible to adversarial attacks that make human-imperceptible perturbations to the data, but result in serious and potentially dangerous prediction errors. To address this issue, practitioners often use adversarial training to learn models that are robust against such attacks at the cost of higher generalization error on unperturbed test sets. The conventional wisdom is that more training data should shrink the gap between the generalization error of adversarially-trained models and standard models. However, we study the training of robust classifiers for both Gaussian and Bernoulli models under $\ell_\infty$ attacks, and we prove that more data may actually increase this gap. Furthermore, our theoretical results identify if and when additional data will finally begin to shrink the gap. Lastly, we experimentally demonstrate that our results also hold for linear regression models, which may indicate that this phenomenon occurs more broadly.