Global Optimality in Distributed Low-rank Matrix Factorization

Zhihui Zhu; Qiuwei Li; Xinshuo Yang; Gongguo Tang; Michael B. Wakin

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arXiv · 1811.03129

Global Optimality in Distributed Low-rank Matrix Factorization

Zhihui Zhu·Qiuwei Li·Xinshuo Yang·Gongguo Tang·Michael B. Wakin

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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.

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BibTeX RIS

Zhihui Zhu, Qiuwei Li, Xinshuo Yang, Gongguo Tang, Michael B. Wakin. 2018-12-24. Global Optimality in Distributed Low-rank Matrix Factorization. https://arxiv.org/abs/1811.03129

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