Convergence rate of entropy-regularized multi-marginal optimal transport costs
Luca Nenna,
Paul Pegon
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
$C\varepsilon \log (1/\varepsilon )+O(\varepsilon )$
for some explicit dimensional constants C depending on the marginals and on the ground cost… Show more
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