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 \textit{Hessian-aware zeroth-order algorithm} called \texttt{ZO-HessAware}. Our theoretical result shows that \texttt{ZO-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.
@article{arxiv.1812.11377,
title = {Hessian-Aware Zeroth-Order Optimization for Black-Box Adversarial Attack},
author = {Haishan Ye and Zhichao Huang and Cong Fang and Chris Junchi Li and Tong Zhang},
journal= {arXiv preprint arXiv:1812.11377},
year = {2019}
}