Optimization and Optimizers for Adversarial Robustness
This work addresses the need for more reliable and general robustness evaluation tools in machine learning, though it is incremental as it builds upon existing packages like AutoAttack.
The paper tackles the problem of evaluating deep learning model robustness against adversarial perturbations by introducing a new algorithmic framework, PWCF, which improves reliability and generality over existing methods, achieving solutions with verified stationarity and feasibility for a wider range of perturbation models.
Empirical robustness evaluation (RE) of deep learning models against adversarial perturbations entails solving nontrivial constrained optimization problems. Existing numerical algorithms that are commonly used to solve them in practice predominantly rely on projected gradient, and mostly handle perturbations modeled by the $\ell_1$, $\ell_2$ and $\ell_\infty$ distances. In this paper, we introduce a novel algorithmic framework that blends a general-purpose constrained-optimization solver PyGRANSO with Constraint Folding (PWCF), which can add more reliability and generality to the state-of-the-art RE packages, e.g., AutoAttack. Regarding reliability, PWCF provides solutions with stationarity measures and feasibility tests to assess the solution quality. For generality, PWCF can handle perturbation models that are typically inaccessible to the existing projected gradient methods; the main requirement is the distance metric to be almost everywhere differentiable. Taking advantage of PWCF and other existing numerical algorithms, we further explore the distinct patterns in the solutions found for solving these optimization problems using various combinations of losses, perturbation models, and optimization algorithms. We then discuss the implications of these patterns on the current robustness evaluation and adversarial training.