Mendelson, Shahar2015-12-100885-064Xhttp://hdl.handle.net/1885/39068We show that under mild assumptions on the learning problem, one can obtain a fast error rate for every reasonable fixed target function even if the base class is not convex. To that end, we show that in such cases the excess loss class satisfies a Bernstein type condition.Keywords: Learning systems; (I ,J) conditions; Base class; Elsevier (CO); Error Rate (ER); excess losses; Learning problems; Nonconvex; Target functions; Error analysis Bernstein condition; Nearest point map; Nonconvex classes200810.1016/j.jco.2007.09.0012015-12-09