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

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 matrix (Hessian), which does not require to even calculate the Hessian. Several other applications of this technique are proposed for speeding up learning, or for eliminating useless parameters.