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    Optimal Algorithms for Decentralized Stochastic Variational Inequalities

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    2202.02771.pdf
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    Description:
    Preprint
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    Type
    Preprint
    Authors
    Kovalev, Dmitry cc
    Beznosikov, Aleksandr
    Sadiev, Abdurakhmon
    Persiianov, Michael
    Richtarik, Peter cc
    Gasnikov, Alexander
    KAUST Department
    Computer Science
    Computer Science Program
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Visual Computing Center (VCC)
    Date
    2022-02-06
    Permanent link to this record
    http://hdl.handle.net/10754/677972
    
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    Abstract
    Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including machine learning problems. This work concentrates on the decentralized setting, which is increasingly important but not well understood. In particular, we consider decentralized stochastic (sum-type) variational inequalities over fixed and time-varying networks. We present lower complexity bounds for both communication and local iterations and construct optimal algorithms that match these lower bounds. Our algorithms are the best among the available literature not only in the decentralized stochastic case, but also in the decentralized deterministic and non-distributed stochastic cases. Experimental results confirm the effectiveness of the presented algorithms.
    Publisher
    arXiv
    arXiv
    2202.02771
    Additional Links
    https://arxiv.org/pdf/2202.02771.pdf
    Collections
    Preprints; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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