The Power of Decaying Steps: Enhancing Attack Stability and Transferability for Sign-based Optimizers

TL;DR

This paper introduces a new approach to improve the stability and transferability of sign-based adversarial attack methods by enforcing decreasing step sizes, supported by theoretical guarantees and extensive experiments.

Contribution

It proposes the MDCS technique for sign-based optimizers, providing theoretical convergence guarantees and demonstrating improved attack transferability and stability.

Findings

MDCS enhances attack transferability across models.

Theoretical proof of optimal convergence rate for MDCS-MI.

Significant empirical improvements over existing methods.

Abstract

Crafting adversarial examples can be formulated as an optimization problem. While sign-based optimizers such as I-FGSM and MI-FGSM have become the de facto standard for the induced optimization problems, there still exist several unsolved problems in theoretical grounding and practical reliability especially in non-convergence and instability, which inevitably influences their transferability. Contrary to the expectation, we observe that the attack success rate may degrade sharply when more number of iterations are conducted. In this paper, we address these issues from an optimization perspective. By reformulating the sign-based optimizer as a specific coordinate-wise gradient descent, we argue that one cause for non-convergence and instability is their non-decaying step-size scheduling. Based upon this viewpoint, we propose a series of new attack algorithms that enforce Monotonically Decreasing Coordinate-wise Step-sizes (MDCS) within sign-based optimizers. Typically, we further provide theoretical guarantees proving that MDCS-MI attains an optimal convergence rate of $O(1/\sqrt{T})$, where $T$ is the number of iterations. Extensive experiments on image classification and cross-modal retrieval tasks demonstrate that our approach not only significantly improves transferability but also enhances attack stability compared to state-of-the-art sign-based methods.