The derivatives of Sinkhorn-Knopp converge
Edouard Pauwels (IRIT, IUF), Samuel Vaiter (CNRS, JAD)
TL;DR
This paper proves that the derivatives of the Sinkhorn-Knopp algorithm converge to those of the entropic regularization of optimal transport, with a locally uniform linear convergence rate.
Contribution
It establishes the convergence properties of derivatives in the Sinkhorn-Knopp algorithm, providing theoretical insights into its stability and accuracy.
Findings
Derivatives of Sinkhorn-Knopp converge to those of entropic optimal transport
Convergence occurs with a locally uniform linear rate
Enhances understanding of algorithm stability and differentiability
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.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Risk and Portfolio Optimization · Optimization and Variational Analysis