Understanding and Mitigating the Tradeoff Between Robustness and Accuracy

TL;DR

This paper analyzes the tradeoff between robustness and accuracy in adversarial training, providing theoretical insights in linear regression and empirical evidence that robust self-training can improve both errors in neural networks.

Contribution

It offers a precise characterization of the robustness-accuracy tradeoff in linear regression and demonstrates that robust self-training enhances both errors in neural networks.

Findings

Standard error can increase even with noiseless optimal predictors.

Robust self-training improves both standard and robust errors in neural networks.

Empirical results show improvements on CIFAR-10 with various adversarial methods.

Abstract

Adversarial training augments the training set with perturbations to improve the robust error (over worst-case perturbations), but it often leads to an increase in the standard error (on unperturbed test inputs). Previous explanations for this tradeoff rely on the assumption that no predictor in the hypothesis class has low standard and robust error. In this work, we precisely characterize the effect of augmentation on the standard error in linear regression when the optimal linear predictor has zero standard and robust error. In particular, we show that the standard error could increase even when the augmented perturbations have noiseless observations from the optimal linear predictor. We then prove that the recently proposed robust self-training (RST) estimator improves robust error without sacrificing standard error for noiseless linear regression. Empirically, for neural networks, we find that RST with different adversarial training methods improves both standard and robust error for random and adversarial rotations and adversarial $\ell_\infty$ perturbations in CIFAR-10.