title: Gradient-based optimization of hyperparameters.
abstract: Many machine learning algorithms can be formulated as the minimization of a training criterion that involves a hyperparameter. This hyperparameter is usually chosen by trial and error with a model selection criterion. In this article we present a methodology to optimize several hyperparameters, based on the computation of the gradient of a model selection criterion with respect to the hyperparameters. In the case of a quadratic training criterion, the gradient of the selection criterion with respect to the hyperparameters is efficiently computed by backpropagating through a Cholesky decomposition. In the more general case, we show that the implicit function theorem can be used to derive a formula for the hyperparameter gradient involving second derivatives of the training criterion.
authors.affiliation: Département d'informatique et recherche opérationnelle, Université de Montréal, Montréal, Québec, Canada, H3C 3J7.
authors.forename: Y
authors.initials: Y
authors.lastname: Bengio
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence