How to Robustify Black-Box ML Models? A Zeroth-Order Optimization Perspective



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The lack of adversarial robustness has been recognized as an important issue for state-of-the-art machine learning (ML) models, e.g., deep neural networks (DNNs). Thereby, robustifying ML models against adversarial attacks is now a major focus of research. However, nearly all existing defense methods, particularly for robust training, made the white-box assumption that the defender has the access to the details of an ML model (or its surrogate alternatives if available), e.g., its architectures and parameters. Beyond existing works, in this paper we aim to address the problem of black-box defense: How to robustify a black-box model using just input queries and output feedback? Such a problem arises in practical scenarios, where the owner of the predictive model is reluctant to share model information in order to preserve privacy. To this end, we propose a general notion of defensive operation that can be applied to black-box models, and design it through the lens of denoised smoothing (DS), a first-order (FO) certified defense technique. To allow the design of merely using model queries, we further integrate DS with the zeroth-order (gradient-free) optimization. However, a direct implementation of zeroth-order (ZO) optimization suffers a high variance of gradient estimates, and thus leads to ineffective defense. To tackle this problem, we next propose to prepend an autoencoder (AE) to a given (black-box) model so that DS can be trained using variance-reduced ZO optimization. We term the eventual defense as ZO-AE-DS. In practice, we empirically show that ZO-AEDS can achieve improved accuracy, certified robustness, and query complexity over existing baselines. And the effectiveness of our approach is justified under both image classification and image reconstruction tasks. Codes are available at

Please cite our work using the BibTeX below.

title={How to Robustify Black-Box {ML} Models? A Zeroth-Order Optimization Perspective},
author={Yimeng Zhang and Yuguang Yao and Jinghan Jia and Jinfeng Yi and Mingyi Hong and Shiyu Chang and Sijia Liu},
booktitle={International Conference on Learning Representations},
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