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- W4383665200 abstract "We investigate the convergence rate of multi-marginal optimal transport costs that are regularized with the Boltzmann-Shannon entropy, as the noise parameter $varepsilon$ tends to $0$. We establish lower and upper bounds on the difference with the unregularized cost of the form $Cvarepsilonlog(1/varepsilon)+O(varepsilon)$ for some explicit dimensional constants $C$ depending on the marginals and on the ground cost, but not on the optimal transport plans themselves. Upper bounds are obtained for Lipschitz costs or locally semi-concave costs for a finer estimate, and lower bounds for $mathcal{C}^2$ costs satisfying some signature condition on the mixed second derivatives that may include degenerate costs, thus generalizing results previously in the two marginals case and for non-degenerate costs. We obtain in particular matching bounds in some typical situations where the optimal plan is deterministic." @default.
- W4383665200 created "2023-07-09" @default.
- W4383665200 creator A5041573575 @default.
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- W4383665200 date "2023-07-06" @default.
- W4383665200 modified "2023-10-09" @default.
- W4383665200 title "Convergence rate of entropy-regularized multi-marginal optimal transport costs" @default.
- W4383665200 doi "https://doi.org/10.48550/arxiv.2307.03023" @default.
- W4383665200 hasPublicationYear "2023" @default.
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