Sample complexity for divergence regularized optimal transport with radial cost
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908902472286208 |
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| author | Han, Ruiyu Wiesel, Johannes |
| author_facet | Han, Ruiyu Wiesel, Johannes |
| contents | We prove a new sample complexity result for divergence regularized optimal transport. Our bound holds for probability measures on~$\mathbb{R}^d$ with exponential tail decay and for radial cost functions that satisfy a local Lipschitz condition. It is sharp up to logarithmic factors, and captures the intrinsic dimension of the marginal distributions through a generalized covering number of their supports. Examples that fit into our framework include subexponential and subgaussian distributions and radial cost functions $c(x,y)=|x-y|^p$ for $p\ge 1$ with logarithmic entropy or polynomial $α$-divergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sample complexity for divergence regularized optimal transport with radial cost Han, Ruiyu Wiesel, Johannes Statistics Theory Probability We prove a new sample complexity result for divergence regularized optimal transport. Our bound holds for probability measures on~$\mathbb{R}^d$ with exponential tail decay and for radial cost functions that satisfy a local Lipschitz condition. It is sharp up to logarithmic factors, and captures the intrinsic dimension of the marginal distributions through a generalized covering number of their supports. Examples that fit into our framework include subexponential and subgaussian distributions and radial cost functions $c(x,y)=|x-y|^p$ for $p\ge 1$ with logarithmic entropy or polynomial $α$-divergence. |
| title | Sample complexity for divergence regularized optimal transport with radial cost |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2510.05685 |