作者：Hundrieser, Shayan; Klatt, Marcel; Munk, Axel
作者单位：University of Gottingen
摘要：For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian process and that the empirical entropic optimal transport value is asymptotically normal. The results are valid for a large class of cost functions and generalize distributional limits for empirical entropic optimal transport quantities on finite spaces. Our pro...
作者：Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：Consider the Monge-Kantorovich problem of transporting densities rho(0) to rho(1) on R-d with a strictly convex cost function. A popular regularization of the problem is the one-parameter family called the entropic cost problem. The entropic cost K-h, h> 0, is significantly faster to compute and hK(h) is known to converge to the optimal transport cost as h goes to zero. We are interested in the rate of convergence. We show that the difference between K-h and 1/ h times the optimal cost of tran...
