Stopped training via algebraic online estimation of the expected test-set error

Stopped training is a method to avoid over-fitting of neural network models by preventing an iterative optimization method from reaching a local minimum of the objective function. It is motivated by the observation that over-fitting occurs gradually as training progresses. The stopping time is typically determined by monitoring the expected generalization performance of the model as approximated by the error on a validation set. In this paper we propose to use an analytic estimate for this purpose. However, these estimates require knowledge of the analytic form of the objective function used for training the network and are only applicable when the weights correspond to a local minimum of this objective function. For this reason, we propose the use of an auxiliary, regularized objective function. The algorithm is “self-contained” and does not require to split the data in a training and a separate validation set