Finite-sample bounds for regularized optimal transport (opens in new tab)

We study the sample complexity of regularized optimal transport for general convex regularizations including the Kullback--Leibler divergence and $L^p$ penalties. Our main results are non-asymptotic bias and variance bounds for the empirical cost, with explicit dependence on the regularization parameter and on the intrinsic dimension of the marginals. Our approach simultaneously improves, unifies, and extends existing finite-sample bounds. In pa...