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    Fastest Rates for Stochastic Mirror Descent Methods

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    1803.07374v1.pdf
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    Description:
    Preprint
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    Type
    Preprint
    Authors
    Hanzely, Filip
    Richtarik, Peter cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2018-03-20
    Permanent link to this record
    http://hdl.handle.net/10754/627407
    
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    Abstract
    Relative smoothness - a notion introduced by Birnbaum et al. (2011) and rediscovered by Bauschke et al. (2016) and Lu et al. (2016) - generalizes the standard notion of smoothness typically used in the analysis of gradient type methods. In this work we are taking ideas from well studied field of stochastic convex optimization and using them in order to obtain faster algorithms for minimizing relatively smooth functions. We propose and analyze two new algorithms: Relative Randomized Coordinate Descent (relRCD) and Relative Stochastic Gradient Descent (relSGD), both generalizing famous algorithms in the standard smooth setting. The methods we propose can be in fact seen as a particular instances of stochastic mirror descent algorithms. One of them, relRCD corresponds to the first stochastic variant of mirror descent algorithm with linear convergence rate.
    Publisher
    arXiv
    arXiv
    arXiv:1803.07374
    Additional Links
    http://arxiv.org/abs/1803.07374v1
    http://arxiv.org/pdf/1803.07374v1
    Collections
    Preprints; Applied Mathematics and Computational Science Program; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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