Quantitative contraction rates for Sinkhorn's algorithm: beyond bounded costs and compact marginals
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911633609064448 |
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| author | Conforti, Giovanni Durmus, Alain Greco, Giacomo |
| author_facet | Conforti, Giovanni Durmus, Alain Greco, Giacomo |
| contents | We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schrödinger potentials, solutions of the quadratic Entropic Optimal Transport problem on $\mathbb{R}^ d$. Our results hold under mild assumptions on the marginal inputs: in particular, we only assume that they admit an asymptotically positive log-concavity profile, covering as special cases log-concave distributions and bounded smooth perturbations of quadratic potentials. Up to the authors' knowledge, these are the first results which establish exponential convergence of Sinkhorn's algorithm in a general setting without assuming bounded cost functions or compactly supported marginals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04451 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantitative contraction rates for Sinkhorn's algorithm: beyond bounded costs and compact marginals Conforti, Giovanni Durmus, Alain Greco, Giacomo Probability Optimization and Control 49Q22, 90C25 (Primary) 49N05, 93E20, 47D07 (Secondary) We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schrödinger potentials, solutions of the quadratic Entropic Optimal Transport problem on $\mathbb{R}^ d$. Our results hold under mild assumptions on the marginal inputs: in particular, we only assume that they admit an asymptotically positive log-concavity profile, covering as special cases log-concave distributions and bounded smooth perturbations of quadratic potentials. Up to the authors' knowledge, these are the first results which establish exponential convergence of Sinkhorn's algorithm in a general setting without assuming bounded cost functions or compactly supported marginals. |
| title | Quantitative contraction rates for Sinkhorn's algorithm: beyond bounded costs and compact marginals |
| topic | Probability Optimization and Control 49Q22, 90C25 (Primary) 49N05, 93E20, 47D07 (Secondary) |
| url | https://arxiv.org/abs/2304.04451 |