A Progressive Batching L-BFGS Method for Machine Learning
Raghu Bollapragada, Jorge Nocedal, Dheevatsa Mudigere, Hao-Jun Shi, Ping Tak Peter Tang
Abstract
The standard L-BFGS method relies on gradient approximations that are not dominated by noise, so that search directions are descent directions, the line search is reliable, and quasi-Newton updating yields useful quadratic models of the objective function. All of this appears to call for a full batch approach, but since small batch sizes give rise to faster algorithms with better generalization properties, L-BFGS is currently not considered an algorithm of choice for large-scale machine learning applications. One need not, however, choose between the two extremes represented by the full batch or highly stochastic regimes, and may instead follow a progressive batching approach in which the sample size increases during the course of the optimization. In this paper, we present a new version of the L-BFGS algorithm that combines three basic components - progressive batching, a stochastic line search, and stable quasi-Newton updating - and that performs well on training logistic regression and deep neural networks. We provide supporting convergence theory for the method.
BibTeX
@InProceedings{pmlr-v80-bollapragada18a,
title = {A Progressive Batching L-{BFGS} Method for Machine Learning},
author = {Bollapragada, Raghu and Nocedal, Jorge and Mudigere, Dheevatsa and Shi, Hao-Jun and Tang, Ping Tak Peter},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
pages = {620--629},
year = {2018},
editor = {Dy, Jennifer and Krause, Andreas},
volume = {80},
series = {Proceedings of Machine Learning Research},
month = {10--15 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v80/bollapragada18a/bollapragada18a.pdf},
url = {https://proceedings.mlr.press/v80/bollapragada18a.html},
abstract = {The standard L-BFGS method relies on gradient approximations that are not dominated by noise, so that search directions are descent directions, the line search is reliable, and quasi-Newton updating yields useful quadratic models of the objective function. All of this appears to call for a full batch approach, but since small batch sizes give rise to faster algorithms with better generalization properties, L-BFGS is currently not considered an algorithm of choice for large-scale machine learning applications. One need not, however, choose between the two extremes represented by the full batch or highly stochastic regimes, and may instead follow a progressive batching approach in which the sample size increases during the course of the optimization. In this paper, we present a new version of the L-BFGS algorithm that combines three basic components - progressive batching, a stochastic line search, and stable quasi-Newton updating - and that performs well on training logistic regression and deep neural networks. We provide supporting convergence theory for the method.}
}