Abstract
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 gradient 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 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.
Original language | English (US) |
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Pages (from-to) | 3142-3150 |
Number of pages | 9 |
Journal | Proceedings of Machine Learning Research |
Volume | 130 |
State | Published - 2021 |
Event | 24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States Duration: Apr 13 2021 → Apr 15 2021 |
ASJC Scopus subject areas
- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability