Globally Optimal On-line Learning Rules

We present a method for determining the globally optimal online learning rule for a soft committee machine under a statistical mechanics framework. This work complements previous results on locally optimal rules, where only the rate of change in generalization the total reduction inerror was considered. We maximize the whole learning process and show howgeneralization error over the resulting rule can significantly outperform the locally optimal rule. 1 Introduction We consider a learning scenario in which a feed-forward neural network model (the an unknown mapping (the teacher), given a set of training examplesstudent) emulates The performance of the student network is typicallyproduced by the teacher. A common form of training is online learning, where training patterns are presented sequentially and independently to the network at each learning step. This form of training can be beneficial in terms of both storage and computation time, especially for large systems.