Learning algorithms for feedforward networks based on finite samples

Abstract

We present two classes of convergent algorithms for learning continuous functions and regressions that are approximated by feedforward networks. The first class of algorithms, applicable to networks with unknown weights located only in the output layer, is obtained by utilizing the potential function methods of Aizerman et al. (1970). The second class, applicable to general feedforward networks, is obtained by utilizing the classical Robbins-Monro style stochastic approximation methods (1951). Conditions relating the sample sizes to the error bounds are derived for both classes of algorithms using martingale-type inequalities. For concreteness, the discussion is presented in terms of neural networks, but the results are applicable to general feedforward networks, in particular to wavelet networks. The algorithms can be directly adapted to concept learning problems.