Global Optimality in Distributed Low-rank Matrix Factorization
Abstract
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization variables appear only locally at a single node in the network. We term the resulting algorithm DGD+LOCAL. Using algorithmic connections to gradient descent and geometric connections to the well-behaved landscape of the centralized low-rank matrix approximation problem, we identify sufficient conditions where DGD+LOCAL is guaranteed to converge with exact consensus to a global minimizer of the original centralized problem. For the distributed low-rank matrix approximation problem, these guarantees are stronger---in terms of consensus and optimality---than what appear in the literature for classical DGD and more general problems.
Cite
@article{arxiv.1811.03129,
title = {Global Optimality in Distributed Low-rank Matrix Factorization},
author = {Zhihui Zhu and Qiuwei Li and Xinshuo Yang and Gongguo Tang and Michael B. Wakin},
journal= {arXiv preprint arXiv:1811.03129},
year = {2018}
}