Boosting Ray Search Procedure of Hard-label Attacks with Transfer-based Priors

One of the most practical and challenging types of black-box adversarial attacks is the hard-label attack, where only the top-1 predicted label is available. One effective approach is to search for the optimal ray direction from the benign image that minimizes the $\ell_p$-norm distance to the adversarial region. The unique advantage of this approach is that it transforms the hard-label attack into a continuous optimization problem. The objective function value is the ray's radius, which can be obtained via binary search at a high query cost. Existing methods use a "sign trick" in gradient estimation to reduce the number of queries. In this paper, we theoretically analyze the quality of this gradient estimation and propose a novel prior-guided approach to improve ray search efficiency both theoretically and empirically. Specifically, we utilize the transfer-based priors from surrogate models, and our gradient estimators appropriately integrate them by approximating the projection of the true gradient onto the subspace spanned by these priors and random directions, in a query-efficient manner. We theoretically derive the expected cosine similarities between the obtained gradient estimators and the true gradient, and demonstrate the improvement achieved by incorporating priors. Extensive experiments on the ImageNet and CIFAR-10 datasets show that our approach significantly outperforms 11 state-of-the-art methods in terms of query efficiency.