Variance Reduced Coordinate Descent with Acceleration: New Method With a Surprising Application to Finite-Sum Problems

Filip Hanzely, Dmitry Kovalev, Peter Richtarik
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:4039-4048, 2020.

Abstract

We propose an accelerated version of stochastic variance reduced coordinate descent – ASVRCD. As other variance reduced coordinate descent methods such as SEGA or SVRCD, our method can deal with problems that include a non-separable and non-smooth regularizer, while accessing a random block of partial derivatives in each iteration only. However, ASVRCD incorporates Nesterov’s momentum, which offers favorable iteration complexity guarantees over both SEGA and SVRCD. As a by-product of our theory, we show that a variant of Katyusha (Allen-Zhu, 2017) is a specific case of ASVRCD, recovering the optimal oracle complexity for the finite sum objective.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-hanzely20b, title = {Variance Reduced Coordinate Descent with Acceleration: New Method With a Surprising Application to Finite-Sum Problems}, author = {Hanzely, Filip and Kovalev, Dmitry and Richtarik, Peter}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {4039--4048}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/hanzely20b/hanzely20b.pdf}, url = {https://proceedings.mlr.press/v119/hanzely20b.html}, abstract = {We propose an accelerated version of stochastic variance reduced coordinate descent – ASVRCD. As other variance reduced coordinate descent methods such as SEGA or SVRCD, our method can deal with problems that include a non-separable and non-smooth regularizer, while accessing a random block of partial derivatives in each iteration only. However, ASVRCD incorporates Nesterov’s momentum, which offers favorable iteration complexity guarantees over both SEGA and SVRCD. As a by-product of our theory, we show that a variant of Katyusha (Allen-Zhu, 2017) is a specific case of ASVRCD, recovering the optimal oracle complexity for the finite sum objective.} }
Endnote
%0 Conference Paper %T Variance Reduced Coordinate Descent with Acceleration: New Method With a Surprising Application to Finite-Sum Problems %A Filip Hanzely %A Dmitry Kovalev %A Peter Richtarik %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-hanzely20b %I PMLR %P 4039--4048 %U https://proceedings.mlr.press/v119/hanzely20b.html %V 119 %X We propose an accelerated version of stochastic variance reduced coordinate descent – ASVRCD. As other variance reduced coordinate descent methods such as SEGA or SVRCD, our method can deal with problems that include a non-separable and non-smooth regularizer, while accessing a random block of partial derivatives in each iteration only. However, ASVRCD incorporates Nesterov’s momentum, which offers favorable iteration complexity guarantees over both SEGA and SVRCD. As a by-product of our theory, we show that a variant of Katyusha (Allen-Zhu, 2017) is a specific case of ASVRCD, recovering the optimal oracle complexity for the finite sum objective.
APA
Hanzely, F., Kovalev, D. & Richtarik, P.. (2020). Variance Reduced Coordinate Descent with Acceleration: New Method With a Surprising Application to Finite-Sum Problems. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:4039-4048 Available from https://proceedings.mlr.press/v119/hanzely20b.html.

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