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    Sinkhorn Algorithm as a Special Case of Stochastic Mirror Descent

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    Type
    Preprint
    Authors
    Mishchenko, Konstantin
    KAUST Department
    Computer Science Program
    Date
    2019-09-16
    Permanent link to this record
    http://hdl.handle.net/10754/660769
    
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    Abstract
    We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and the objective function. Since the problem has unbounded domain, the objective function is neither smooth nor it has bounded gradients. However, one can still approach the problem using the notion of relative smoothness, obtaining that the stochastic objective is 1-relative smooth. The discovered equivalence allows us to propose 1) new methods for optimal transport, 2) an extension of Sinkhorn algorithm beyond two constraints.
    Publisher
    arXiv
    arXiv
    1909.06918
    Additional Links
    https://arxiv.org/pdf/1909.06918
    Collections
    Preprints; Computer Science Program

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