Estimates of the Approximation Error Using Rademacher Complexity: Learning Vector-Valued Functions

For certain families of multivariable vector-valued functions to be approximated, the accuracy of approximation schemes made up of linear combinations of computational units containing adjustable parameters is investigated. Upper bounds on the approximation error are derived that depend on the Rademacher complexities of the families. The estimates exploit possible relationships among the components of the multivariable vector-valued functions. All such components are approximated simultaneously in such a way to use, for a desired approximation accuracy, less computational units than those required by componentwise approximation. An application to N-stage optimization problems is discussed.