Convergent on-line algorithms for supervised learning in neural networks

We define online algorithms for neural network training, based on the construction of multiple copies of the network, which are trained by employing different data blocks. It is shown that suitable training algorithms can be defined, in a way that the disagreement between the different copies of the network is asymptotically reduced, and convergence toward stationary points of the global error function can be guaranteed. Relevant features of the proposed approach are that the learning rate must be not necessarily forced to zero and that real-time learning is permitted.