Accelerating Greedy Coordinate Descent Methods

Haihao Lu, Robert Freund, Vahab Mirrokni
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:3257-3266, 2018.

Abstract

We introduce and study two algorithms to accelerate greedy coordinate descent in theory and in practice: Accelerated Semi-Greedy Coordinate Descent (ASCD) and Accelerated Greedy Coordinate Descent (AGCD). On the theory side, our main results are for ASCD: we show that ASCD achieves $O(1/k^2)$ convergence, and it also achieves accelerated linear convergence for strongly convex functions. On the empirical side, while both AGCD and ASCD outperform Accelerated Randomized Coordinate Descent on most instances in our numerical experiments, we note that AGCD significantly outperforms the other two methods in our experiments, in spite of a lack of theoretical guarantees for this method. To complement this empirical finding for AGCD, we present an explanation why standard proof techniques for acceleration cannot work for AGCD, and we further introduce a technical condition under which AGCD is guaranteed to have accelerated convergence. Finally, we confirm that this technical condition holds in our numerical experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-lu18b, title = {Accelerating Greedy Coordinate Descent Methods}, author = {Lu, Haihao and Freund, Robert and Mirrokni, Vahab}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {3257--3266}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/lu18b/lu18b.pdf}, url = {https://proceedings.mlr.press/v80/lu18b.html}, abstract = {We introduce and study two algorithms to accelerate greedy coordinate descent in theory and in practice: Accelerated Semi-Greedy Coordinate Descent (ASCD) and Accelerated Greedy Coordinate Descent (AGCD). On the theory side, our main results are for ASCD: we show that ASCD achieves $O(1/k^2)$ convergence, and it also achieves accelerated linear convergence for strongly convex functions. On the empirical side, while both AGCD and ASCD outperform Accelerated Randomized Coordinate Descent on most instances in our numerical experiments, we note that AGCD significantly outperforms the other two methods in our experiments, in spite of a lack of theoretical guarantees for this method. To complement this empirical finding for AGCD, we present an explanation why standard proof techniques for acceleration cannot work for AGCD, and we further introduce a technical condition under which AGCD is guaranteed to have accelerated convergence. Finally, we confirm that this technical condition holds in our numerical experiments.} }
Endnote
%0 Conference Paper %T Accelerating Greedy Coordinate Descent Methods %A Haihao Lu %A Robert Freund %A Vahab Mirrokni %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-lu18b %I PMLR %P 3257--3266 %U https://proceedings.mlr.press/v80/lu18b.html %V 80 %X We introduce and study two algorithms to accelerate greedy coordinate descent in theory and in practice: Accelerated Semi-Greedy Coordinate Descent (ASCD) and Accelerated Greedy Coordinate Descent (AGCD). On the theory side, our main results are for ASCD: we show that ASCD achieves $O(1/k^2)$ convergence, and it also achieves accelerated linear convergence for strongly convex functions. On the empirical side, while both AGCD and ASCD outperform Accelerated Randomized Coordinate Descent on most instances in our numerical experiments, we note that AGCD significantly outperforms the other two methods in our experiments, in spite of a lack of theoretical guarantees for this method. To complement this empirical finding for AGCD, we present an explanation why standard proof techniques for acceleration cannot work for AGCD, and we further introduce a technical condition under which AGCD is guaranteed to have accelerated convergence. Finally, we confirm that this technical condition holds in our numerical experiments.
APA
Lu, H., Freund, R. & Mirrokni, V.. (2018). Accelerating Greedy Coordinate Descent Methods. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:3257-3266 Available from https://proceedings.mlr.press/v80/lu18b.html.

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