We study the problem of learning halfspaces with Massart noise in the distribution-specific PAC model. We give the first computationally efficient algorithm for this problem with respect to a broad family of distributions, including log-concave distributions. This resolves an open question posed in a number of prior works. Our approach is extremely simple: We identify a smooth {\em non-convex} surrogate loss with the property that any approximate stationary point of this loss defines a halfspace that is close to the target halfspace. Given this structural result, we can use SGD to solve the underlying learning problem.
@article{arxiv.2002.05632,
title = {Learning Halfspaces with Massart Noise Under Structured Distributions},
author = {Ilias Diakonikolas and Vasilis Kontonis and Christos Tzamos and Nikos Zarifis},
journal= {arXiv preprint arXiv:2002.05632},
year = {2020}
}