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Distributed Low-rank Matrix Factorization With Exact Consensus
Zhihui Zhu · Qiuwei Li · Xinshuo Yang · Gongguo Tang · Michael B Wakin

Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #212

Low-rank matrix factorization is a problem of broad importance, owing to the ubiquity of low-rank models in machine learning contexts. In spite of its non- convexity, this problem has a well-behaved geometric landscape, permitting local search algorithms such as gradient descent to converge to global minimizers. In this paper, we study low-rank matrix factorization in the distributed setting, where local variables at each node encode parts of the overall matrix factors, and consensus is encouraged among certain such variables. We identify conditions under which this new problem also has a well-behaved geometric landscape, and we propose an extension of distributed gradient descent (DGD) to solve this problem. The favorable landscape allows us to prove convergence to global optimality with exact consensus, a stronger result than what is provided by off-the-shelf DGD theory.

Author Information

Zhihui Zhu (Johns Hopkins University)
Qiuwei Li (Colorado School of Mines)
Xinshuo Yang (Colorado School of Mines)
Gongguo Tang (Colorado School of Mines)

Gongguo Tang is an Assistant Professor in the Department of Electrical Engineering at Colorado School of Mines since 2014. Before that, he was a visiting scholar at Simons Institute for the Theory of Computing at University of California, Berkeley in Fall 2013 and a postdoc working with Professor Robert Nowak at the University of Wisconsin-Madison and Professor Benjamin Recht at the University of California, Berkeley from August 2011 to December 2013. He received his Ph.D. in Electrical Engineering from Washington University in St. Louis under the supervision of Professor Arye Nehorai.

Michael B Wakin (Colorado School of Mines)

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