Stronger and Faster Wasserstein Adversarial Attacks
This work addresses the problem of improving adversarial attack robustness for deep learning models, particularly in computer vision, by introducing more efficient methods under the Wasserstein metric, representing an incremental advancement in optimization techniques for adversarial attacks.
The paper tackles the challenge of constructing effective adversarial attacks under the Wasserstein metric, which is computationally demanding, by developing efficient optimization algorithms that lead to stronger and faster attacks, reducing a residual network's accuracy on CIFAR-10 to 3.4% within a Wasserstein perturbation radius of 0.005, compared to 65.6% with previous methods.
Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to "small, imperceptible" perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the $\ell_p$ metric, Wasserstein distance, which takes geometry in pixel space into account, has long been known to be a suitable metric for measuring image quality and has recently risen as a compelling alternative to the $\ell_p$ metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show that the Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to $3.4\%$ within a Wasserstein perturbation ball of radius $0.005$, in contrast to $65.6\%$ using the previous Wasserstein attack based on an \emph{approximate} projection operator. Furthermore, employing our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models.