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    Smoothness Matrices Beat Smoothness Constants: Better Communication Compression Techniques for Distributed Optimization

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    2102.07245.pdf
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    Type
    Preprint
    Authors
    Safaryan, Mher cc
    Hanzely, Filip
    Richtarik, Peter cc
    KAUST Department
    Computer Science Program
    Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
    Visual Computing Center (VCC)
    Date
    2021-02-14
    Permanent link to this record
    http://hdl.handle.net/10754/667470
    
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    Abstract
    Large scale distributed optimization has become the default tool for the training of supervised machine learning models with a large number of parameters and training data. Recent advancements in the field provide several mechanisms for speeding up the training, including {\em compressed communication}, {\em variance reduction} and {\em acceleration}. However, none of these methods is capable of exploiting the inherently rich data-dependent smoothness structure of the local losses beyond standard smoothness constants. In this paper, we argue that when training supervised models, {\em smoothness matrices} -- information-rich generalizations of the ubiquitous smoothness constants -- can and should be exploited for further dramatic gains, both in theory and practice. In order to further alleviate the communication burden inherent in distributed optimization, we propose a novel communication sparsification strategy that can take full advantage of the smoothness matrices associated with local losses. To showcase the power of this tool, we describe how our sparsification technique can be adapted to three distributed optimization algorithms -- DCGD, DIANA and ADIANA -- yielding significant savings in terms of communication complexity. The new methods always outperform the baselines, often dramatically so.
    Publisher
    arXiv
    arXiv
    2102.07245
    Additional Links
    https://arxiv.org/pdf/2102.07245
    Collections
    Preprints; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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