A Formal Approach to Optimally Configure a Fully Connected Multilayer Hybrid Neural Network

This paper is devoted to a novel formal analysis, optimizing the learning models for feedforward multilayer neural networks with hybrid structures. The proposed mathematical description replicates a specific switched-type optimal control problem (OCP). We have developed an equivalent, optimal control-based formulation of the given problem of training a hybrid feedforward multilayer neural network, to train the target mapping function constrained by the training samples. This novel formal approach makes it possible to apply some well-established optimal control techniques to design a versatile type of full connection neural networks. We next discuss the irrelevance of the necessity of Pontryagin-type optimality conditions for the construction of the obtained switched-type OCP. This fact motivated us to consider the so-called direct-solution approaches to the switched OCPs, which can be associated with the learning of hybrid neural networks. Concretely, we consider the generalized reduced-gradient algorithm in the framework of the auxiliary switched OCP.