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

Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020)

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Ilias Diakonikolas, Daniel M. Kane, Pasin Manurangsi


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 $2 \leq p < \infty$.