A Simple Trick for Estimating the Weight Decay Parameter

We present a simple trick to get an approximate estimate of the weight decay parameter λ. The method combines early stopping and weight decay, into the estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \hat \lambda = ||\nabla E(W_{es} )||/||2W_{es} ||, $$\end{document} where Wes is the set of weights at the early stopping point, and E(W) is the training data fit error. The estimate is demonstrated and compared to the standard cross-validation procedure for λ selection on one synthetic and four real life data sets. The result is that λ is as good an estimator for the optimal weight decay parameter value as the standard search estimate, but orders of magnitude quicker to compute. The results also show that weight decay can produce solutions that are significantly superior to committees of networks trained with early stopping.