Neural networks learning as a multiobjective optimal control problem

Abstract

The supervised learning process of multilayer feedforward neural networks can be considered as a class of multi-objective, multi-stage optimal control problem. An iterative parametric minimax method is proposed in which the original optimization problem is embedded into a weighted minimax formulation. The resulting auxiliary parametric optimization problems at the lower level have simple structures that are readily tackled by efficient solution methods, such as the dynamic programming or the error backpropagation algorithm. The analytical expression of the partial derivatives of systems performance indices with respect to the weighting vector in the parametric minimax formulation is derived.