Many factorization models like matrix or tensor factorization have been proposed for the important application of recommender systems. The success of such factorization models depends largely on the choice of good values for the regularization parameters. Without a careful selection they result in poor prediction quality as they either underfit or overfit the data. Regularization values are typically determined by an expensive search that requires learning the model parameters several times: once for each tuple of candidate values for the regularization parameters. In this paper, we present a new method that adapts the regularization automatically while training the model parameters. To achieve this, we optimize simultaneously for two criteria: (1) as usual the model parameters for the regularized objective and (2) the regularization of future parameter updates for the best predictive quality on a validation set. We develop this for the generic model class of Factorization Machines ...