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Adversarial testing methods based on Projected Gradient Descent (PGD) arewidely used for searching norm-bounded perturbations that cause the inputs ofneural networks to be misclassified. This paper takes a deeper look at thesemethods and explains the effect of different hyperparameters (i.e., optimizer,step size and surrogate loss). We introduce the concept of MultiTargetedtesting, which makes clever use of alternative surrogate losses, and explainwhen and how MultiTargeted is guaranteed to find optimal perturbations.Finally, we demonstrate that MultiTargeted outperforms more sophisticatedmethods and often requires less iterative steps than other variants of PGDfound in the literature. Notably, MultiTargeted ranks first on MadryLab'swhite-box MNIST and CIFAR-10 leaderboards, reducing the accuracy of their MNISTmodel to 88.36% (with $\ell_\infty$ perturbations of $\epsilon = 0.3$) and theaccuracy of their CIFAR-10 model to 44.03% (at $\epsilon = 8/255$).MultiTargeted also ranks first on the TRADES leaderboard reducing the accuracyof their CIFAR-10 model to 53.07% (with $\ell_\infty$ perturbations of$\epsilon = 0.031$).

An Alternative Surrogate Loss for PGD-based Adversarial Testing