Robust binary classification with the 01 loss

TL;DR

This paper introduces a stochastic coordinate descent algorithm for 01 loss classifiers, demonstrating comparable accuracy to convex loss models and enhanced robustness against adversarial attacks across multiple image benchmarks.

Contribution

The paper develops a novel stochastic coordinate descent method for 01 loss neural networks, showing improved adversarial robustness while maintaining competitive accuracy.

Findings

01 loss classifiers are more robust to adversarial attacks than convex loss models.

The proposed algorithm is fast and achieves accuracy comparable to SVMs and logistic models.

Adversarial training further enhances robustness without sacrificing test accuracy.

Abstract

The 01 loss is robust to outliers and tolerant to noisy data compared to convex loss functions. We conjecture that the 01 loss may also be more robust to adversarial attacks. To study this empirically we have developed a stochastic coordinate descent algorithm for a linear 01 loss classifier and a single hidden layer 01 loss neural network. Due to the absence of the gradient we iteratively update coordinates on random subsets of the data for fixed epochs. We show our algorithms to be fast and comparable in accuracy to the linear support vector machine and logistic loss single hidden layer network for binary classification on several image benchmarks, thus establishing that our method is on-par in test accuracy with convex losses. We then subject them to accurately trained substitute model black box attacks on the same image benchmarks and find them to be more robust than convex counterparts. On CIFAR10 binary classification task between classes 0 and 1 with adversarial perturbation of 0.0625 we see that the MLP01 network loses 27\% in accuracy whereas the MLP-logistic counterpart loses 83\%. Similarly on STL10 and ImageNet binary classification between classes 0 and 1 the MLP01 network loses 21\% and 20\% while MLP-logistic loses 67\% and 45\% respectively. On MNIST that is a well-separable dataset we find MLP01 comparable to MLP-logistic and show under simulation how and why our 01 loss solver is less robust there. We then propose adversarial training for our linear 01 loss solver that significantly improves its robustness on MNIST and all other datasets and retains clean test accuracy. Finally we show practical applications of our method to deter traffic sign and facial recognition adversarial attacks. We discuss attacks with 01 loss, substitute model accuracy, and several future avenues like multiclass, 01 loss convolutions, and further adversarial training.