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    Variance Reduced Coordinate Descent with Acceleration: New Method With a Surprising Application to Finite-Sum Problems

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    Type
    Preprint
    Authors
    Hanzely, Filip
    Kovalev, Dmitry
    Richtarik, Peter cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Computer Science
    Computer Science Program
    Date
    2020-02-11
    Permanent link to this record
    http://hdl.handle.net/10754/666019
    
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    Abstract
    We propose an accelerated version of stochastic variance reduced coordinate descent -- ASVRCD. As other variance reduced coordinate descent methods such as SEGA or SVRCD, our method can deal with problems that include a non-separable and non-smooth regularizer, while accessing a random block of partial derivatives in each iteration only. However, ASVRCD incorporates Nesterov's momentum, which offers favorable iteration complexity guarantees over both SEGA and SVRCD. As a by-product of our theory, we show that a variant of Allen-Zhu (2017) is a specific case of ASVRCD, recovering the optimal oracle complexity for the finite sum objective.
    Sponsors
    The authors would like to express their gratitude to Konstantin Mishchenko. In particular, Konstantin has introduced us to the product space objective (13) and at the same time, the idea that SAGA is a special case of SEGA was born during the discussion with him.
    Publisher
    arXiv
    arXiv
    2002.04670
    Additional Links
    https://arxiv.org/pdf/2002.04670
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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