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Non-ConvexSGDLearns Halfspaceswith AdversarialLabelNoise

Neural Information Processing Systems

We study the problem of agnostically learning homogeneous halfspaces in the distribution-specific PAC model. For a broad family of structured distributions, including log-concave distributions, we show that non-convex SGD efficiently convergestoasolution withmisclassification errorO(opt)+,whereoptisthe misclassification error of the best-fitting halfspace.