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We consider the problem of estimating an unknown function from noisy observations on a random grid. In this paper we address the following aggregation problem: given functions , find an “aggregated ”estimator which approximates nearly as well as the best convex combination of . We propose algorithms which provide approximations of with expected accuracy . We show that this approximation rate cannot be significantly improved. We discuss two specific applications: nonparametric prediction for a dynamic system with output nonlinearity and reconstruction in the Jones – Barron class.