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    Optimal and Practical Algorithms for Smooth and Strongly Convex Decentralized Optimization

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    Type
    Preprint
    Authors
    Kovalev, Dmitry
    Salim, Adil
    Richtarik, Peter cc
    KAUST Department
    Computer Science
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Visual Computing Center (VCC)
    Computer Science Program
    Date
    2020-06-21
    Permanent link to this record
    http://hdl.handle.net/10754/666022
    
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    Abstract
    We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication rounds required to achieve $\varepsilon$ accuracy have recently been proven. We propose two new algorithms for this decentralized optimization problem and equip them with complexity guarantees. We show that our first method is optimal both in terms of the number of communication rounds and in terms of the number of gradient computations. Unlike existing optimal algorithms, our algorithm does not rely on the expensive evaluation of dual gradients. Our second algorithm is optimal in terms of the number of communication rounds, without a logarithmic factor. Our approach relies on viewing the two proposed algorithms as accelerated variants of the Forward Backward algorithm to solve monotone inclusions associated with the decentralized optimization problem. We also verify the efficacy of our methods against state-of-the-art algorithms through numerical experiments.
    Publisher
    arXiv
    arXiv
    2006.11773
    Additional Links
    https://arxiv.org/pdf/2006.11773
    Collections
    Preprints; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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