We consider the sample complexity of agnostic learning with respect to squared loss. It is known that if the function class F used for learning is convex then one can obtain better sample complexity bounds than usual. It has been claimed that there is a lower bound that showed there was an essential gap in the rate. In this paper we show that the lower bound proof has a gap in it. Although we do not provide a definitive answer to its validity. More positively, we show one can obtain "fast" sample complexity bounds for nonconvex F for "most" target conditional expectations. The new bounds depend on the detailed geometry of F, in particular the distance in a certain sense of the target's conditional expectation from the set of nonuniqueness points of the class F.
CITATION STYLE
Mendelson, S., & Williamson, R. C. (2002). Agnostic learning nonconvex function classes. In Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science) (Vol. 2375, pp. 1–13). Springer Verlag. https://doi.org/10.1007/3-540-45435-7_1
Mendeley helps you to discover research relevant for your work.