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    SEGA: Variance Reduction via Gradient Sketching

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    1809.03054.pdf
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    Description:
    Preprint
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    Type
    Preprint
    Authors
    Hanzely, Filip
    Mishchenko, Konstantin cc
    Richtarik, Peter cc
    KAUST Department
    Applied Mathematics and Computational Science
    Applied Mathematics and Computational Science Program
    Computer Science
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2018-09-09
    Permanent link to this record
    http://hdl.handle.net/10754/653114
    
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    Abstract
    We propose a randomized first order optimization method--SEGA (SkEtchedGrAdient method)-- which progressively throughout its iterations builds avariance-reduced estimate of the gradient from random linear measurements(sketches) of the gradient obtained from an oracle. In each iteration, SEGAupdates the current estimate of the gradient through a sketch-and-projectoperation using the information provided by the latest sketch, and this issubsequently used to compute an unbiased estimate of the true gradient througha random relaxation procedure. This unbiased estimate is then used to perform agradient step. Unlike standard subspace descent methods, such as coordinatedescent, SEGA can be used for optimization problems with a non-separableproximal term. We provide a general convergence analysis and prove linearconvergence for strongly convex objectives. In the special case of coordinatesketches, SEGA can be enhanced with various techniques such as importancesampling, minibatching and acceleration, and its rate is up to a small constantfactor identical to the best-known rate of coordinate descent.
    Publisher
    arXiv
    arXiv
    1809.03054
    Additional Links
    https://arxiv.org/pdf/1809.03054
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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