Papers
Topics
Authors
Recent
Assistant
AI Research Assistant
Well-researched responses based on relevant abstracts and paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses.
Gemini 2.5 Flash
Gemini 2.5 Flash 164 tok/s
Gemini 2.5 Pro 46 tok/s Pro
GPT-5 Medium 21 tok/s Pro
GPT-5 High 27 tok/s Pro
GPT-4o 72 tok/s Pro
Kimi K2 204 tok/s Pro
GPT OSS 120B 450 tok/s Pro
Claude Sonnet 4.5 34 tok/s Pro
2000 character limit reached

Global Optimality in Distributed Low-rank Matrix Factorization (1811.03129v2)

Published 7 Nov 2018 in math.OC, cs.LG, and stat.ML

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.

Citations (4)

Summary

We haven't generated a summary for this paper yet.

Lightbulb Streamline Icon: https://streamlinehq.com

Continue Learning

We haven't generated follow-up questions for this paper yet.

List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.