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We perform a comprehensive study on the performance of derivative freeoptimization (DFO) algorithms for the generation of targeted black-boxadversarial attacks on Deep Neural Network (DNN) classifiers assuming theperturbation energy is bounded by an $\ell_\infty$ constraint and the number ofqueries to the network is limited. This paper considers four pre-existingstate-of-the-art DFO-based algorithms along with the introduction of a newalgorithm built on BOBYQA, a model-based DFO method. We compare thesealgorithms in a variety of settings according to the fraction of images thatthey successfully misclassify given a maximum number of queries to the DNN.  The experiments disclose how the likelihood of finding an adversarial exampledepends on both the algorithm used and the setting of the attack; algorithmslimiting the search of adversarial example to the vertices of the $\ell^\infty$constraint work particularly well without structural defenses, while thepresented BOBYQA based algorithm works better for especially small perturbationenergies. This variance in performance highlights the importance of newalgorithms being compared to the state-of-the-art in a variety of settings, andthe effectiveness of adversarial defenses being tested using as wide a range ofalgorithms as possible.

An Empirical Study of Derivative-Free-Optimization Algorithms for Targeted Black-Box Attacks in Deep Neural Networks