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The derivatives of Sinkhorn-Knopp converge

Optimization and Control 2022-08-04 v2 Machine Learning
Authors: Edouard Pauwels , Samuel Vaiter
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Abstract

We show that the derivatives of the Sinkhorn-Knopp algorithm, or iterative proportional fitting procedure, converge towards the derivatives of the entropic regularization of the optimal transport problem with a locally uniform linear convergence rate.

Keywords

sinkhorn-knopp algorithm iterative proportional fitting derivatives convergence entropic regularization optimal transport linear convergence rate

Cite

@article{arxiv.2207.12717,
  title  = {The derivatives of Sinkhorn-Knopp converge},
  author = {Edouard Pauwels and Samuel Vaiter},
  journal= {arXiv preprint arXiv:2207.12717},
  year   = {2022}
}

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