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We consider the problem of adaptation to the margin in binary classification.We suggest a penalized empirical risk minimization classifier that adaptivelyattains, up to a logarithmic factor, fast optimal rates of convergence for theexcess risk, that is, rates that can be faster than n^{-1/2}, where n is thesample size. We show that our method also gives adaptive estimators for theproblem of edge estimation.

Square root penalty: Adaptation to the margin in classification and in edge estimation