An OT problem regularized by an f-divergence shares the same unique minimizer as one regularized by a g-divergence after cost transformation, shown for Polish spaces with bounded costs.
Smooth and sparse optimal transport,
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Equivalence of optimal transport problems to regularization on the family of f-divergences
An OT problem regularized by an f-divergence shares the same unique minimizer as one regularized by a g-divergence after cost transformation, shown for Polish spaces with bounded costs.