Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods

Robert Gower, Nicolas Le Roux, Francis Bach
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:707-715, 2018.

Abstract

Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation of the control variates and leading to faster theoretical convergence close to the optimum. We then propose accurate and computationally efficient approximations to the Hessian, both using a diagonal and a low-rank matrix. Finally, we demonstrate the effectiveness of our method on a wide range of problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-gower18a, title = {Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods}, author = {Gower, Robert and Le Roux, Nicolas and Bach, Francis}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {707--715}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/gower18a/gower18a.pdf}, url = {https://proceedings.mlr.press/v84/gower18a.html}, abstract = {Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation of the control variates and leading to faster theoretical convergence close to the optimum. We then propose accurate and computationally efficient approximations to the Hessian, both using a diagonal and a low-rank matrix. Finally, we demonstrate the effectiveness of our method on a wide range of problems.} }
Endnote
%0 Conference Paper %T Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods %A Robert Gower %A Nicolas Le Roux %A Francis Bach %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-gower18a %I PMLR %P 707--715 %U https://proceedings.mlr.press/v84/gower18a.html %V 84 %X Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation of the control variates and leading to faster theoretical convergence close to the optimum. We then propose accurate and computationally efficient approximations to the Hessian, both using a diagonal and a low-rank matrix. Finally, we demonstrate the effectiveness of our method on a wide range of problems.
APA
Gower, R., Le Roux, N. & Bach, F.. (2018). Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:707-715 Available from https://proceedings.mlr.press/v84/gower18a.html.

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