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    SAGA with Arbitrary Sampling

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    1901.08669.pdf
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    Description:
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    Type
    Preprint
    Authors
    Qian, Xu
    Qu, Zheng
    Richtarik, Peter cc
    KAUST Department
    Computer Science
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-01-24
    Permanent link to this record
    http://hdl.handle.net/10754/653121
    
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    Abstract
    We study the problem of minimizing the average of a very large number ofsmooth functions, which is of key importance in training supervised learningmodels. One of the most celebrated methods in this context is the SAGAalgorithm. Despite years of research on the topic, a general-purpose version ofSAGA---one that would include arbitrary importance sampling and minibatchingschemes---does not exist. We remedy this situation and propose a general andflexible variant of SAGA following the {\em arbitrary sampling} paradigm. Weperform an iteration complexity analysis of the method, largely possible due tothe construction of new stochastic Lyapunov functions. We establish linearconvergence rates in the smooth and strongly convex regime, and under aquadratic functional growth condition (i.e., in a regime not assuming strongconvexity). Our rates match those of the primal-dual method Quartz for which anarbitrary sampling analysis is available, which makes a significant steptowards closing the gap in our understanding of complexity of primal and dualmethods for finite sum problems.
    Publisher
    arXiv
    arXiv
    1901.08669
    Additional Links
    https://arxiv.org/pdf/1901.08669
    Collections
    Preprints; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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