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Mind the Box: l1-APGD for Sparse Adversarial Attacks on Image Classifiers
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:2201-2211, 2021.
Abstract
We show that when taking into account also the image domain [0,1]d, established l1-projected gradient descent (PGD) attacks are suboptimal as they do not consider that the effective threat model is the intersection of the l1-ball and [0,1]d. We study the expected sparsity of the steepest descent step for this effective threat model and show that the exact projection onto this set is computationally feasible and yields better performance. Moreover, we propose an adaptive form of PGD which is highly effective even with a small budget of iterations. Our resulting l1-APGD is a strong white-box attack showing that prior works overestimated their l1-robustness. Using l1-APGD for adversarial training we get a robust classifier with SOTA l1-robustness. Finally, we combine l1-APGD and an adaptation of the Square Attack to l1 into l1-AutoAttack, an ensemble of attacks which reliably assesses adversarial robustness for the threat model of l1-ball intersected with [0,1]d.