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Expander Graph and Communication-Efficient Decentralized Optimization

Yat Tin Chow(ytchow***at***math.ucla.edu)
Wei Shi(wilburs***at***bu.edu)
Tianyu Wu(wuty11***at***math.ucla.edu)
Wotao Yin(wotaoyin***at***math.ucla.edu)

Abstract: In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy. We discover that the so-called expander graphs are near-optimal choices. We propose three approaches to construct expander graphs for different numbers of nodes and node degrees. Our numerical results show that the performance of decentralized optimization is significantly better on expander graphs than other regular graphs.

Keywords: decentralized optimization, expander graphs, Ramanujan graphs, communication efficiency.

Category 1: Network Optimization

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: UCLA CAM Report 16-83

Download: [PDF]

Entry Submitted: 12/02/2016
Entry Accepted: 12/31/2017
Entry Last Modified: 12/02/2016

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