Equivalence of optimal transport problems to regularization on the family of f-divergences
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914501452890112 |
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| author | Nicaise, Maxime Bermudez, Yaiza Perlaza, Samir M. |
| author_facet | Nicaise, Maxime Bermudez, Yaiza Perlaza, Samir M. |
| contents | This work establishes that an optimal transport~(OT) problem regularized by a given $f$-divergence admits the same solution as another OT problem regularized by a different $g$-divergence, under an appropriate transformation of the cost function. This structural equivalence between OT problems regularized by distinct divergences, in the sense of sharing the same unique minimizer, is demonstrated within the framework of Polish spaces with bounded cost functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12996 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivalence of optimal transport problems to regularization on the family of f-divergences Nicaise, Maxime Bermudez, Yaiza Perlaza, Samir M. Statistics Theory This work establishes that an optimal transport~(OT) problem regularized by a given $f$-divergence admits the same solution as another OT problem regularized by a different $g$-divergence, under an appropriate transformation of the cost function. This structural equivalence between OT problems regularized by distinct divergences, in the sense of sharing the same unique minimizer, is demonstrated within the framework of Polish spaces with bounded cost functions. |
| title | Equivalence of optimal transport problems to regularization on the family of f-divergences |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2604.12996 |