{"ID":2859214,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.05685","arxiv_id":"2510.05685","title":"Sample complexity for divergence regularized optimal transport with radial cost","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2510.05685","url_pdf":"https://arxiv.org/pdf/2510.05685v3","authors":"[\"Ruiyu Han\",\"Johannes Wiesel\"]","published":"2025-10-07T08:41:29Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}