Gradient estimation and vector space projection have been studied as two distinct topics. We aim to bridge the gap between the two by investigating how to efficiently estimate gradient based on a projected low-dimensional space. We first provide lower and upper bounds for gradient estimation under both linear and nonlinear projections, and outline checkable sufficient conditions under which one is better than the other. Moreover, we analyze the query complexity for the projection-based gradient estimation and present a sufficient condition for query-efficient estimators. Built upon our theoretic analysis, we propose a novel query-efficient Nonlinear Gradient Projection-based Boundary Blackbox Attack (NonLinear-BA). We conduct extensive experiments on four image datasets: ImageNet, CelebA, CIFAR-10, and MNIST, and show the superiority of the proposed methods compared with the state-of-the-art baselines. In particular, we show that the projection-based boundary blackbox attacks are able to achieve much smaller magnitude of perturbations with 100% attack success rate based on efficient queries. Both linear and nonlinear projections demonstrate their advantages under different conditions. We also evaluate NonLinear-BA against the commercial online API MEGVII Face++, and demonstrate the high blackbox attack performance both quantitatively and qualitatively. The code is publicly available at https://github.com/AI-secure/NonLinear-BA.

本文探讨了如何在项目的低维空间中高效地估计梯度，并提供了一个高效的非线性梯度投影边界黑盒攻击方案和其在多个数据集上的优越性能的演示和评估。

基于非线性投影的梯度估计方法，用于查询高效的黑盒攻击