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.

Inthis paper,werely onabroader viewofpropercompositelosses and arecent construct from information geometry,sourcefunctions, whose fitting alleviates constraints faced by canonical links.