Stability of Schrödinger potentials and convergence of Sinkhorn’s algorithm
Stability of Schrödinger potentials and convergence of Sinkhorn’s algorithm
We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schrödinger potentials, describing the density of the optimal couplings. When the marginals converge in total variation, the optimal couplings also converge in total variation. This …