Practical Quasi-Newton Methods for Training Deep Neural Networks

Donald Goldfarb, Yi Ren, Achraf Bahamou

Spotlight presentation: Orals & Spotlights Track 18: Deep Learning
on 2020-12-09T07:10:00-08:00 - 2020-12-09T07:20:00-08:00
Poster Session 4 (more posters)
on 2020-12-09T09:00:00-08:00 - 2020-12-09T11:00:00-08:00
GatherTown: Deep learning ( Town C1 - Spot A3 )
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Abstract: We consider the development of practical stochastic quasi-Newton, and in particular Kronecker-factored block diagonal BFGS and L-BFGS methods, for training deep neural networks (DNNs). In DNN training, the number of variables and components of the gradient n is often of the order of tens of millions and the Hessian has n^2 elements. Consequently, computing and storing a full n times n BFGS approximation or storing a modest number of (step, change in gradient) vector pairs for use in an L-BFGS implementation is out of the question. In our proposed methods, we approximate the Hessian by a block-diagonal matrix and use the structure of the gradient and Hessian to further approximate these blocks, each of which corresponds to a layer, as the Kronecker product of two much smaller matrices. This is analogous to the approach in KFAC , which computes a Kronecker-factored block diagonal approximation to the Fisher matrix in a stochastic natural gradient method. Because the indefinite and highly variable nature of the Hessian in a DNN, we also propose a new damping approach to keep the upper as well as the lower bounds of the BFGS and L-BFGS approximations bounded. In tests on autoencoder feed-forward network models with either nine or thirteen layers applied to three datasets, our methods outperformed or performed comparably to KFAC and state-of-the-art first-order stochastic methods.

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