Combinatorial Preconditioners for Proximal Algorithms on Graphs
Abstract
We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We prove that certain decompositions lead to a theoretically optimal condition number. We also show how ideal decompositions can be realized using matroid partitioning and propose efficient greedy variants thereof for large-scale problems. Coupled with specialized solvers for the resulting scaled proximal subproblems, the preconditioned algorithm achieves competitive performance in machine learning and vision applications.
Cite
Text
Möllenhoff et al. "Combinatorial Preconditioners for Proximal Algorithms on Graphs." International Conference on Artificial Intelligence and Statistics, 2018.Markdown
[Möllenhoff et al. "Combinatorial Preconditioners for Proximal Algorithms on Graphs." International Conference on Artificial Intelligence and Statistics, 2018.](https://mlanthology.org/aistats/2018/mollenhoff2018aistats-combinatorial/)BibTeX
@inproceedings{mollenhoff2018aistats-combinatorial,
title = {{Combinatorial Preconditioners for Proximal Algorithms on Graphs}},
author = {Möllenhoff, Thomas and Ye, Zhenzhang and Wu, Tao and Cremers, Daniel},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2018},
pages = {38-47},
url = {https://mlanthology.org/aistats/2018/mollenhoff2018aistats-combinatorial/}
}