The Complexity of Adversarially Robust Proper Learning of Halfspaces with Agnostic Noise
Ilias Diakonikolas, Daniel M. Kane, Pasin Manurangsi · arXiv (Cornell University) · 2020
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 $2 \leq p < \infty$.