# The LogBarrier adversarial attack: making effective use of decision boundary information

## TL;DR

This paper introduces the LogBarrier adversarial attack, a gradient-based method using the logarithmic barrier technique to generate minimal perturbations for fooling image classifiers, outperforming existing attacks especially on difficult images.

## Contribution

The paper presents a novel untargeted adversarial attack leveraging the logarithmic barrier method, incorporating best practices from optimization literature for the first time.

## Key findings

- Achieves similar or better attack distances than state-of-the-art methods on benchmark datasets.
- Performs significantly better on challenging images requiring larger perturbations.
- More efficiently perturbs images on defended models, reducing the needed perturbation distance.

## Abstract

Adversarial attacks for image classification are small perturbations to images that are designed to cause misclassification by a model. Adversarial attacks formally correspond to an optimization problem: find a minimum norm image perturbation, constrained to cause misclassification. A number of effective attacks have been developed. However, to date, no gradient-based attacks have used best practices from the optimization literature to solve this constrained minimization problem. We design a new untargeted attack, based on these best practices, using the established logarithmic barrier method. On average, our attack distance is similar or better than all state-of-the-art attacks on benchmark datasets (MNIST, CIFAR10, ImageNet-1K). In addition, our method performs significantly better on the most challenging images, those which normally require larger perturbations for misclassification. We employ the LogBarrier attack on several adversarially defended models, and show that it adversarially perturbs all images more efficiently than other attacks: the distance needed to perturb all images is significantly smaller with the LogBarrier attack than with other state-of-the-art attacks.