Almost-sharp $O(k^{-1} \log k)$ convergence rate for the Sinkhorn algorithm in the asymptotically scalable case
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917493120958464 |
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| author | Wang, Guillaume |
| author_facet | Wang, Guillaume |
| contents | 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 $Ω(k^{-1})$ (Qu et al., 2025) and the previously best known upper bound $O(k^{-1/2})$ (Léger, 2021), and generalizes the analysis for the positive case by Dvurechensky et al. (2018). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26265 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Almost-sharp $O(k^{-1} \log k)$ convergence rate for the Sinkhorn algorithm in the asymptotically scalable case Wang, Guillaume Optimization and Control 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 $Ω(k^{-1})$ (Qu et al., 2025) and the previously best known upper bound $O(k^{-1/2})$ (Léger, 2021), and generalizes the analysis for the positive case by Dvurechensky et al. (2018). |
| title | Almost-sharp $O(k^{-1} \log k)$ convergence rate for the Sinkhorn algorithm in the asymptotically scalable case |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2604.26265 |