Domain decomposition for entropy regularized optimal transport

Abstract We study Benamou’s domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that variant converges to globally solution under very mild assumptions. prove linear convergence of with respect Kullback–Leibler divergence and illustrate (potentially slow) rates numerical examples. On problems sufficient geometric structure (such as Wasserstein distances between images) we expect much faster convergence. then discuss important aspects a computationally efficient implementation, such adaptive sparsity, coarse-to-fine scheme parallelization, paving way numerically solving large-scale problems. demonstrate performance computing Wasserstein-2 distance 2D images observe that, even without compares favorably applying single implementation Sinkhorn terms runtime, memory quality.