Hessian-Aware Zeroth-Order Optimization for Black-Box Adversarial Attack

Zeroth-order optimization is an important research topic in machine learning. In recent years, it has become a key tool in black-box adversarial attack to neural network based image classifiers. However, existing zeroth-order optimization algorithms rarely extract second-order information of the model function. In this paper, we utilize the second-order information of the objective function and propose a novel textitHessian-aware zeroth-order algorithm called textttZO-HessAware. Our theoretical result shows that textttZO-HessAware has an improved zeroth-order convergence rate and query complexity under structured Hessian approximation, where we propose a few approximation methods for estimating Hessian. Our empirical studies on the black-box adversarial attack problem validate that our algorithm can achieve improved success rates with a lower query complexity.