Learning in neural networks by normalized stochastic gradient algorithm: local convergence

In this paper, a normalized stochastic gradient algorithm is proposed for learning in feedforward neural networks. By using a new methodology based on the martingale convergence results, asymptotic properties of the algorithm are analyzed. It is proved that, in general, the sequence of the algorithm states converges with probability one to the set of zeroes of the gradient of the criterion function locally on the event where it is bounded. Then, these results are applied to learning in multilayer perceptrons.