Aggregation by Exponential Weighting and Sharp Oracle Inequalities

Arnak S. Dalalyan, Alexandre B. Tsybakov

Abstract: In the present paper, we study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp oracle inequalities for convex aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We show how these results can be applied to derive a sparsity oracle inequality.