A Self-Correcting Variable-Metric Algorithm for Stochastic Optimization

Frank Curtis
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:632-641, 2016.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T A Self-Correcting Variable-Metric Algorithm for Stochastic Optimization %A Frank Curtis %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-curtis16 %I PMLR %P 632--641 %U https://proceedings.mlr.press/v48/curtis16.html %V 48 %X 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.
RIS
TY - CPAPER TI - A Self-Correcting Variable-Metric Algorithm for Stochastic Optimization AU - Frank Curtis BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-curtis16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 632 EP - 641 L1 - http://proceedings.mlr.press/v48/curtis16.pdf UR - https://proceedings.mlr.press/v48/curtis16.html AB - 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. ER -
APA
Curtis, F.. (2016). A Self-Correcting Variable-Metric Algorithm for Stochastic Optimization. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:632-641 Available from https://proceedings.mlr.press/v48/curtis16.html.

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