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We develop a fast and reliable method for solving large-scale optimaltransport (OT) problems at an unprecedented combination of speed and accuracy.Built on the celebrated Douglas-Rachford splitting technique, our methodtackles the original OT problem directly instead of solving an approximateregularized problem, as many state-of-the-art techniques do. This allows us toprovide sparse transport plans and avoid numerical issues of methods that useentropic regularization. The algorithm has the same cost per iteration as thepopular Sinkhorn method, and each iteration can be executed efficiently, inparallel. The proposed method enjoys an iteration complexity $O(1/\epsilon)$compared to the best-known $O(1/\epsilon^2)$ of the Sinkhorn method. Inaddition, we establish a linear convergence rate for our formulation of the OTproblem. We detail an efficient GPU implementation of the proposed method thatmaintains a primal-dual stopping criterion at no extra cost. Substantialexperiments demonstrate the effectiveness of our method, both in terms ofcomputation times and robustness.

A Fast and Accurate Splitting Method for Optimal Transport: Analysis and Implementation