Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms

Qianxiao Li, Cheng Tai, Weinan E
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:2101-2110, 2017.

Abstract

We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together with optimal control theory to derive novel adaptive hyper-parameter adjustment policies. Our algorithms have competitive performance with the added benefit of being robust to varying models and datasets. This provides a general methodology for the analysis and design of stochastic gradient algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-li17f, title = {Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms}, author = {Qianxiao Li and Cheng Tai and Weinan E}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {2101--2110}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/li17f/li17f.pdf}, url = {https://proceedings.mlr.press/v70/li17f.html}, abstract = {We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together with optimal control theory to derive novel adaptive hyper-parameter adjustment policies. Our algorithms have competitive performance with the added benefit of being robust to varying models and datasets. This provides a general methodology for the analysis and design of stochastic gradient algorithms.} }
Endnote
%0 Conference Paper %T Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms %A Qianxiao Li %A Cheng Tai %A Weinan E %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-li17f %I PMLR %P 2101--2110 %U https://proceedings.mlr.press/v70/li17f.html %V 70 %X We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together with optimal control theory to derive novel adaptive hyper-parameter adjustment policies. Our algorithms have competitive performance with the added benefit of being robust to varying models and datasets. This provides a general methodology for the analysis and design of stochastic gradient algorithms.
APA
Li, Q., Tai, C. & E, W.. (2017). Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:2101-2110 Available from https://proceedings.mlr.press/v70/li17f.html.

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