Abstract
Regularization is an essential technique to improve generalization of neural networks. Traditionally, regularization is conduced by including an additional term in the cost function of a learning algorithm. One main drawback of these regularization techniques is that a hyperparameter that determines to which extension the regularization influences the learning algorithm must be determined beforehand. This paper addresses the neural network regularization problem from a multi-objective optimization point of view. During the optimization, both structure and parameters of the neural network will be optimized. A slightly modified version of two multi-objective optimization algorithms, the dynamic weighted aggregation (DWA) method and the elitist non-dominated sorting genetic algorithm (NSGA-II) are used and compared. An evolutionary multi-objective approach to neural network regularization has a number of advantages compared to the traditional methods. First, a number of models with a spectrum of model complexity can be obtained in one optimization run instead of only one single solution. Second, an efficient new regularization term can be introduced, which is not applicable to gradient-based learning algorithms. As a natural by-product of the multi-objective optimization approach to neural network regularization, neural network ensembles can be easily constructed using the obtained networks with different levels of model complexity. Thus, the model complexity of the ensemble can be adjusted by adjusting the weight of each member network in the ensemble. Simulations are carried out on a test function to illustrate the feasibility of the proposed ideas.