Non-ConvexSGDLearns Halfspaceswith AdversarialLabelNoise

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.