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What is Learnable in Valiant's Theory of the Learnable? 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Equivalence of optimal transport problems to regularization on the family of f-divergences
Maxime Nicaise, Yaiza Bermudez, Samir M. Perlaza · 2026-04-15 · via math.ST updates on arXiv.org

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.

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