Decision-based attacks (DBA), wherein attackers perturb inputs to spoof
learning algorithms by observing solely the output labels, are a type of severe
adversarial attacks against Deep Neural Networks (DNNs) requiring minimal
knowledge of attackers. State-of-the-art DBA attacks relying on zeroth-order
gradient estimation require an excessive number of queries. Recently, Bayesian
optimization (BO) has shown promising in reducing the number of queries in
score-based attacks (SBA), in which attackers need to observe real-valued
probability scores as outputs. However, extending BO to the setting of DBA is
nontrivial because in DBA only output labels instead of real-valued scores, as
needed by BO, are available to attackers. In this paper, we close this gap by
proposing an efficient DBA attack, namely BO-DBA. Different from existing
approaches, BO-DBA generates adversarial examples by searching so-called
emph{directions of perturbations}. It then formulates the problem as a BO
problem that minimizes the real-valued distortion of perturbations. With the
optimized perturbation generation process, BO-DBA converges much faster than
the state-of-the-art DBA techniques. Experimental results on pre-trained
ImageNet classifiers show that BO-DBA converges within 200 queries while the
state-of-the-art DBA techniques need over 15,000 queries to achieve the same
level of perturbation distortion. BO-DBA also shows similar attack success
rates even as compared to BO-based SBA attacks but with less distortion.

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