  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.
