Almost-sharp $O(k^{-1} \log k)$ convergence rate for the Sinkhorn algorithm in the asymptotically scalable case

Guillaume Wang

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arXiv · 2604.26265

Almost-sharp $O(k^{-1} \log k)$ convergence rate for the Sinkhorn algorithm in the asymptotically scalable case

Guillaume Wang

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Abstract

We prove that the Sinkhorn algorithm converges at a rate of $O(k^{-1} \log k)$ in $\ell_1$-norm marginal error, in the asymptotically scalable case. This almost closes the gap between the lower bound $\Omega(k^{-1})$ (Qu et al., 2025) and the previously best known upper bound $O(k^{-1/2})$ (L\'eger, 2021), and generalizes the analysis for the positive case by Dvurechensky et al. (2018).

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BibTeX RIS

Guillaume Wang. 2026-04-29. Almost-sharp $O(k^{-1} \log k)$ convergence rate for the Sinkhorn algorithm in the asymptotically scalable case. https://arxiv.org/abs/2604.26265

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