LMI formulation for multiobjective learning in Radial Basis Function neural networks

This work presents a Linear Matrix Inequality (LMI) formulation for training Radial Basis Function (RBF) neural networks, considering the context of multiobjective learning. The multiobjective learning approach treats the bias-variance dilemma in neural network modeling as a bi-objective optimization problem: the minimization of the empirical risk measured by the sum of squared error over the training data, and the minimization of the structure complexity measured by the norm of the weight vector. We transform the multiobjective problem into a constrained mono-objective one, using the ∈-constraint method. This mono-objective problem can be efficiently solved using an LMI formulation. A procedure for choosing the width parameter of the radial basis functions is also presented. The results show that the proposed methodology provides generalization control and high quality solutions.