A Self-Correcting Variable-Metric Algorithm for Stochastic Optimization
Abstract
An algorithm for stochastic (convex or nonconvex) optimization is presented. The algorithm is variable-metric in the sense that, in each iteration, the step is computed through the product of a symmetric positive definite scaling matrix and a stochastic (mini-batch) gradient of the objective function, where the sequence of scaling matrices is updated dynamically by the algorithm. A key feature of the algorithm is that it does not overly restrict the manner in which the scaling matrices are updated. Rather, the algorithm exploits fundamental self-correcting properties of BFGS-type updating—properties that have been over-looked in other attempts to devise quasi-Newton methods for stochastic optimization. Numerical experiments illustrate that the method and a limited memory variant of it are stable and outperform (mini-batch) stochastic gradient and other quasi-Newton methods when employed to solve a few machine learning problems.
BibTeX
@InProceedings{pmlr-v48-curtis16,
title = {A Self-Correcting Variable-Metric Algorithm for Stochastic Optimization},
author = {Curtis, Frank},
booktitle = {Proceedings of The 33rd International Conference on Machine Learning},
pages = {632--641},
year = {2016},
editor = {Balcan, Maria Florina and Weinberger, Kilian Q.},
volume = {48},
series = {Proceedings of Machine Learning Research},
address = {New York, New York, USA},
month = {20--22 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v48/curtis16.pdf},
url = {https://proceedings.mlr.press/v48/curtis16.html},
abstract = {An algorithm for stochastic (convex or nonconvex) optimization is presented. The algorithm is variable-metric in the sense that, in each iteration, the step is computed through the product of a symmetric positive definite scaling matrix and a stochastic (mini-batch) gradient of the objective function, where the sequence of scaling matrices is updated dynamically by the algorithm. A key feature of the algorithm is that it does not overly restrict the manner in which the scaling matrices are updated. Rather, the algorithm exploits fundamental self-correcting properties of BFGS-type updating—properties that have been over-looked in other attempts to devise quasi-Newton methods for stochastic optimization. Numerical experiments illustrate that the method and a limited memory variant of it are stable and outperform (mini-batch) stochastic gradient and other quasi-Newton methods when employed to solve a few machine learning problems.}
}