Nonlinear Projection Based Gradient Estimation for Query Efficient Blackbox Attacks

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 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.

arXiv commentAccepted by AISTATS 2021; 9 pages excluding references and appendices

References in corpus (6)

• Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks
• Transferability in Machine Learning: from Phenomena to Black-Box Attacks using Adversarial Samples
• Delving into Transferable Adversarial Examples and Black-box Attacks
• The Space of Transferable Adversarial Examples
• Decision-Based Adversarial Attacks: Reliable Attacks Against Black-Box Machine Learning Models
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Cited by in corpus (3)

• Towards Visual Distortion in Black-Box Attacks
• TRS: Transferability Reduced Ensemble via Encouraging Gradient Diversity and Model Smoothness
• Rethinking Image-Scaling Attacks: The Interplay Between Vulnerabilities in Machine Learning Systems