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We study the problem of learning halfspaces with Massart noise in thedistribution-specific PAC model. We give the first computationally efficientalgorithm for this problem with respect to a broad family of distributions,including log-concave distributions. This resolves an open question posed in anumber of prior works. Our approach is extremely simple: We identify a smooth{\em non-convex} surrogate loss with the property that any approximatestationary point of this loss defines a halfspace that is close to the targethalfspace. Given this structural result, we can use SGD to solve the underlyinglearning problem.

Learning Halfspaces with Massart Noise Under Structured Distributions