Mind the box: l_1-APGD for sparse adversarial attacks on image classifiers
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We show that when taking into account also the image domain [0,1]^d, established l_1-projected gradient descent (PGD) attacks are suboptimal as they do not consider that the effective threat model is the intersection of the l_1-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 l_1-APGD is a strong white box attack showing that prior work overestimated their l_1-robustness. Using l_1-APGD for adversarial training we get a robust classifier with SOTA l_1-robustness. Finally, we combine l_1-APGD and an adaptation of the Square Attack to l_1 into l_1-AutoAttack, an ensemble of attacks which reliably assesses adversarial robustness for the threat model of l_1-ball intersected with [0,1]^d.
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