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    A Linearly Convergent Algorithm for Decentralized Optimization: Sending Less Bits for Free!

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    Type
    Preprint
    Authors
    Kovalev, Dmitry
    Koloskova, Anastasia
    Jaggi, Martin
    Richtarik, Peter
    Stich, Sebastian U.
    KAUST Department
    Computer Science
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2020-11-03
    Permanent link to this record
    http://hdl.handle.net/10754/665879
    
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    Abstract
    Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the entire system. We propose a new randomized first-order method which tackles the communication bottleneck by applying randomized compression operators to the communicated messages. By combining our scheme with a new variance reduction technique that progressively throughout the iterations reduces the adverse effect of the injected quantization noise, we obtain the first scheme that converges linearly on strongly convex decentralized problems while using compressed communication only. We prove that our method can solve the problems without any increase in the number of communications compared to the baseline which does not perform any communication compression while still allowing for a significant compression factor which depends on the conditioning of the problem and the topology of the network. Our key theoretical findings are supported by numerical experiments.
    Publisher
    arXiv
    arXiv
    2011.01697
    Additional Links
    https://arxiv.org/pdf/2011.01697
    Collections
    Preprints; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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