Title: Query-Efficient Hard-label Black-box Attack: An Optimization-based Approach. Abstract: We study the problem of attacking machine learning models in the hard-label black-box setting, where no model information is revealed except that the attacker can make queries to probe the corresponding hard-label decisions. This is a very challenging problem since the direct extension of state-of-the-art white-box attacks (e.g., C&W or PGD) to the hard-label black-box setting will require minimizing a non-continuous step function, which is combinatorial and cannot be solved by a gradient-based optimizer. The only two current approaches are based on random walk on the boundary (Brendel et al., 2017) and random trials to evaluate the loss function (Ilyas et al., 2018), which require lots of queries and lacks convergence guarantees. 
We propose a novel way to formulate the hard-label black-box attack as a real-valued optimization problem which is usually continuous and can be solved by any zeroth order optimization algorithm. For example, using the Randomized Gradient-Free method (Nesterov & Spokoiny, 2017), we are able to bound the number of iterations needed for our algorithm to achieve stationary points under mild assumptions. We demonstrate that our proposed method outperforms the previous stochastic approaches to attacking convolutional neural networks on MNIST, CIFAR, and ImageNet datasets. More interestingly, we show that the proposed algorithm can also be used to attack other discrete and non-continuous machine learning models, such as Gradient Boosting Decision Trees (GBDT).