Early stopping

Even though it's a pure regularization technique, early stopping is often considered as a last resort when all other approaches to prevent overfitting and maximize validation accuracy fail. In many cases (above all, in deep learning scenarios), it's possible to observe a typical behavior of the training process considering both training and the validation cost functions:

 Example of early stopping before the beginning of ascending phase of U-curve

During the first epochs, both costs decrease, but it can happen that after a threshold epoch e_s, the validation cost starts increasing. If we continue with the training process, this results in overfitting the training set and increasing the variance. For this reason, when there are no other options, it's possible to prematurely stop the training process. In order to do so, it's necessary to store the last parameter vector before the beginning of a new iteration and, in the case of no improvements or the accuracy worsening, to stop the process and recover the last parameters. As explained, this procedure must never be considered as the best choice, because a better model or an improved dataset could yield higher performances. With early stopping, there's no way to verify alternatives, therefore it must be adopted only at the last stage of the process and never at the beginning. Many deep learning frameworks such as Keras include helpers to implement an early stopping callback; however, it's important to check whether the last parameter vector is the one stored before the last epoch or the one corresponding to e_s. In this case, it could be useful to repeat the training process, stopping it at the epoch previous to e_s (where the minimum validation cost has been achieved).