  We study the computational complexity of adversarially robust proper learning
of halfspaces in the distribution-independent agnostic PAC model, with a focus
on $L_p$ 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 $L_{\infty}$ perturbations
case is provably computationally harder than the case $2 \leq p < \infty$.
