Automatic Learning Rate Maximization by On-Line Estimation of the Hessian's Eigenvectors

Part of Advances in Neural Information Processing Systems 5 (NIPS 1992)

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Yann LeCun, Patrice Simard, Barak Pearlmutter


We propose a very simple, and well principled way of computing the optimal step size in gradient descent algorithms. The on-line version is very efficient computationally, and is applicable to large backpropagation networks trained on large data sets. The main ingredient is a technique for estimating the principal eigenvalue(s) and eigenvector(s) of the objective function's second derivative ma(cid:173) trix (Hessian), which does not require to even calculate the Hes(cid:173) sian. Several other applications of this technique are proposed for speeding up learning, or for eliminating useless parameters.