Improving the Convergence Rate of Ray Search Optimization for Query-Efficient Hard-Label Attacks

TL;DR

This paper introduces ARS-OPT and PARS-OPT, momentum-based algorithms that significantly improve the convergence rate and query efficiency of hard-label black-box adversarial attacks by optimizing ray search directions.

Contribution

The paper proposes a novel momentum-based optimization method, ARS-OPT, and an enhanced version, PARS-OPT, for more efficient hard-label adversarial attacks, supported by theoretical analysis and extensive experiments.

Findings

ARS-OPT achieves faster convergence than existing methods.

PARS-OPT incorporates surrogate priors for further acceleration.

Our methods outperform 13 state-of-the-art approaches in query efficiency.

Abstract

In hard-label black-box adversarial attacks, where only the top-1 predicted label is accessible, the prohibitive query complexity poses a major obstacle to practical deployment. In this paper, we focus on optimizing a representative class of attacks that search for the optimal ray direction yielding the minimum $\ell_2$-norm perturbation required to move a benign image into the adversarial region. Inspired by Nesterov's Accelerated Gradient (NAG), we propose a momentum-based algorithm, ARS-OPT, which proactively estimates the gradient with respect to a future ray direction inferred from accumulated momentum. We provide a theoretical analysis of its convergence behavior, showing that ARS-OPT enables more accurate directional updates and achieves faster, more stable optimization. To further accelerate convergence, we incorporate surrogate-model priors into ARS-OPT's gradient estimation, resulting in PARS-OPT with enhanced performance. The superiority of our approach is supported by theoretical guarantees under standard assumptions. Extensive experiments on ImageNet and CIFAR-10 demonstrate that our method surpasses 13 state-of-the-art approaches in query efficiency.