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Expander Graph and Communication-Efficient Decentralized Optimization

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arxiv 1612.00903 v1 pith:ISXCEQ6Q submitted 2016-12-03 math.OC cs.DCcs.MA

Yat-Tin Chow , Wei Shi , Tianyu Wu , Wotao Yin This is my paper · ORCID
classification math.OCcs.DCcs.MA
keywords expandergraphsdecentralizedoptimizationcommunicationgraphaccuracyachieve
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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.

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