Empirical risk minimization is optimal for the convex aggregation problem
نویسنده
چکیده
Let F be a finite model of cardinality M and denote by conv(F ) its convex hull. The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over conv(F ). Consider the bounded regression model with respect to the squared risk denoted by R(·). If f̂ ERM-C n denotes the empirical risk minimization procedure over conv(F ), then we prove that for any x > 0, with probability greater than 1 − 4 exp(−x),
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