Alternating Randomized Block Coordinate Descent
Jelena Diakonikolas, Lorenzo Orecchia
Abstract
Block-coordinate descent algorithms and alternating minimization methods are fundamental optimization algorithms and an important primitive in large-scale optimization and machine learning. While various block-coordinate-descent-type methods have been studied extensively, only alternating minimization – which applies to the setting of only two blocks – is known to have convergence time that scales independently of the least smooth block. A natural question is then: is the setting of two blocks special? We show that the answer is “no” as long as the least smooth block can be optimized exactly – an assumption that is also needed in the setting of alternating minimization. We do so by introducing a novel algorithm AR-BCD, whose convergence time scales independently of the least smooth (possibly non-smooth) block. The basic algorithm generalizes both alternating minimization and randomized block coordinate (gradient) descent, and we also provide its accelerated version – AAR-BCD.
BibTeX
@InProceedings{pmlr-v80-diakonikolas18a,
title = {Alternating Randomized Block Coordinate Descent},
author = {Diakonikolas, Jelena and Orecchia, Lorenzo},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
pages = {1224--1232},
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/diakonikolas18a/diakonikolas18a.pdf},
url = {https://proceedings.mlr.press/v80/diakonikolas18a.html},
abstract = {Block-coordinate descent algorithms and alternating minimization methods are fundamental optimization algorithms and an important primitive in large-scale optimization and machine learning. While various block-coordinate-descent-type methods have been studied extensively, only alternating minimization – which applies to the setting of only two blocks – is known to have convergence time that scales independently of the least smooth block. A natural question is then: is the setting of two blocks special? We show that the answer is “no” as long as the least smooth block can be optimized exactly – an assumption that is also needed in the setting of alternating minimization. We do so by introducing a novel algorithm AR-BCD, whose convergence time scales independently of the least smooth (possibly non-smooth) block. The basic algorithm generalizes both alternating minimization and randomized block coordinate (gradient) descent, and we also provide its accelerated version – AAR-BCD.}
}