The Complexity of Adversarially Robust Proper Learning of Halfspaces with Agnostic Noise

We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent agnostic PAC model, with a focus on $\ell_p$ perturbations. We give a computationally efficient learning algorithm and a nearly matching computational hardness result for this problem. An interesting implication of our findings is that the $\ell_{\infty}$ perturbations case is provably computationally harder than the case $1 < p < \infty$.