Even Faster Accelerated Coordinate Descent Using Non-Uniform Sampling

Zeyuan Allen-Zhu, Zheng Qu, Peter Richtarik, Yang Yuan
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:1110-1119, 2016.

Abstract

Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent that is one of the central methods used in machine learning. In this paper, we improve the best known running time of accelerated coordinate descent by a factor up to \sqrtn. Our improvement is based on a clean, novel non-uniform sampling that selects each coordinate with a probability proportional to the square root of its smoothness parameter. Our proof technique also deviates from the classical estimation sequence technique used in prior work. Our speed-up applies to important problems such as empirical risk minimization and solving linear systems, both in theory and in practice.

Cite this Paper


BibTeX
@InProceedings{pmlr-v48-allen-zhuc16, title = {Even Faster Accelerated Coordinate Descent Using Non-Uniform Sampling}, author = {Allen-Zhu, Zeyuan and Qu, Zheng and Richtarik, Peter and Yuan, Yang}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {1110--1119}, 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/allen-zhuc16.pdf}, url = { http://proceedings.mlr.press/v48/allen-zhuc16.html }, abstract = {Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent that is one of the central methods used in machine learning. In this paper, we improve the best known running time of accelerated coordinate descent by a factor up to \sqrtn. Our improvement is based on a clean, novel non-uniform sampling that selects each coordinate with a probability proportional to the square root of its smoothness parameter. Our proof technique also deviates from the classical estimation sequence technique used in prior work. Our speed-up applies to important problems such as empirical risk minimization and solving linear systems, both in theory and in practice.} }
Endnote
%0 Conference Paper %T Even Faster Accelerated Coordinate Descent Using Non-Uniform Sampling %A Zeyuan Allen-Zhu %A Zheng Qu %A Peter Richtarik %A Yang Yuan %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-allen-zhuc16 %I PMLR %P 1110--1119 %U http://proceedings.mlr.press/v48/allen-zhuc16.html %V 48 %X Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent that is one of the central methods used in machine learning. In this paper, we improve the best known running time of accelerated coordinate descent by a factor up to \sqrtn. Our improvement is based on a clean, novel non-uniform sampling that selects each coordinate with a probability proportional to the square root of its smoothness parameter. Our proof technique also deviates from the classical estimation sequence technique used in prior work. Our speed-up applies to important problems such as empirical risk minimization and solving linear systems, both in theory and in practice.
RIS
TY - CPAPER TI - Even Faster Accelerated Coordinate Descent Using Non-Uniform Sampling AU - Zeyuan Allen-Zhu AU - Zheng Qu AU - Peter Richtarik AU - Yang Yuan 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-allen-zhuc16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 1110 EP - 1119 L1 - http://proceedings.mlr.press/v48/allen-zhuc16.pdf UR - http://proceedings.mlr.press/v48/allen-zhuc16.html AB - Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent that is one of the central methods used in machine learning. In this paper, we improve the best known running time of accelerated coordinate descent by a factor up to \sqrtn. Our improvement is based on a clean, novel non-uniform sampling that selects each coordinate with a probability proportional to the square root of its smoothness parameter. Our proof technique also deviates from the classical estimation sequence technique used in prior work. Our speed-up applies to important problems such as empirical risk minimization and solving linear systems, both in theory and in practice. ER -
APA
Allen-Zhu, Z., Qu, Z., Richtarik, P. & Yuan, Y.. (2016). Even Faster Accelerated Coordinate Descent Using Non-Uniform Sampling. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:1110-1119 Available from http://proceedings.mlr.press/v48/allen-zhuc16.html .

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