An adaptive learning rate for the training of B-spline networks

In the training of B-spline networks, iterative gradient method with a constant learning rate are often used. It is well-known that the training speed depends on the choice of the learning rate, yet few guidelines in the selection of a suitable learning rate are available in the literature. In this paper, an adaptive learning rate to update the weights of a B-spline network with a scalar or multi-output is proposed. It is shown that under certain conditions, the performance index for a training algorithm using the proposed adaptive learning rate converges to a constant as the number of iterations increases. Also, a method for computing the criterion for terminating the training is presented. Simulation examples are presented, showing that training of the networks using the adaptive training is much faster than that using a constant learning rate.