On the optimality of the empirical risk minimization procedure for the convex aggregation problem
We study the performance of (ERM), with respect to the quadratic risk, in the context of , in which one wants to construct a procedure whose risk is as close as possible to the best function in the convex hull of an arbitrary finite class . We show that ERM performed in the convex hull of is an optimal aggregation procedure for the convex aggregation problem. We also show that if this procedure is used for the problem of model selection aggregation, in which one wants to mimic the performance...