Accelerating greedy coordinate descent methods
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1806.02476.pdf
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Author(s)
Lu, Haihao
Freund, Robert Michael
Mirrokni Banadaki, Vahab Seyed
Date Issued
July 2018
Journal
Proceedings of Machine Learning Research
Publisher
Proceedings of Machine Learning Research
Citation
Lu, Haihao, Robert Freund, and Vahab Mirrokni. "Accelerating Greedy Coordinate Descent Methods." Proceedings of Machine Learning Research, 80 (2018): 3257-3266.
Version
Author's final manuscript
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 Co-ordinate Descent (AGCD). On the theory side, our main results are for ASCD: We show that ASCD achieves 0(l/k[superscript 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 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Sloan School of Management
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http://proceedings.mlr.press/v80/lu18b.html
