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- W4287201888 abstract "We study the potential functions that determine the optimal density for $varepsilon$-entropically regularized optimal transport, the so-called Schrodinger potentials, and their convergence to the counterparts in classical optimal transport, the Kantorovich potentials. In the limit $varepsilonto0$ of vanishing regularization, strong compactness holds in $L^{1}$ and cluster points are Kantorovich potentials. In particular, the Schrodinger potentials converge in $L^{1}$ to the Kantorovich potentials as soon as the latter are unique. These results are proved for all continuous, integrable cost functions on Polish spaces. In the language of Schrodinger bridges, the limit corresponds to the small-noise regime." @default.
- W4287201888 created "2022-07-25" @default.
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- W4287201888 date "2021-04-23" @default.
- W4287201888 modified "2023-09-30" @default.
- W4287201888 title "Entropic Optimal Transport: Convergence of Potentials" @default.
- W4287201888 doi "https://doi.org/10.48550/arxiv.2104.11720" @default.
- W4287201888 hasPublicationYear "2021" @default.
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