288 pp. per issue
6 x 9, illustrated
2014 Impact factor:

Neural Computation

August 1, 2000, Vol. 12, No. 8, Pages 1889-1900
(doi: 10.1162/089976600300015187)
© 2000 Massachusetts Institute of Technology
Gradient-Based Optimization of Hyperparameters
Article PDF (73.8 KB)

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 hyper-parameters, 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 hyper-parameter gradient involving second derivatives of the training criterion.