Convergence analysis on the deterministic mini-batch learning algorithm for noise resilient radial basis function networks

This paper gives a formal convergence analysis on the mini-batch training algorithm for noise resilient radial basis function (RBF) networks. Unlike the conventional analysis which assumes that the mini-batch process is operated in a stochastic manner, we consider that the mini-batch training process is operated in a deterministic manner. The deterministic process divides the training samples into a number of fixed mini-batches, and the mini-batches are presented in a fixed order. This paper first states the noise resilient objective function for weight noise and weight fault. We then derive the mini-batch training algorithm for this noise resilient objective function. Our main contribution is the convergence analysis on the mini-batch training algorithm. We show that under the deterministic setting, the mini-batch training algorithm converges. The converged weight vector is asymptotically close to the optimal batch mode solution. Also, we derive the sufficient conditions (the learning rate range) for convergence. Our theoretical results can be applied to not only the noise resilient objective function but also a large class of objective functions.