- Keywords: Optimal transport, Operator splitting, Douglas-Rachford, ADMM, GPUs
- Abstract: We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting, our method tackles the original OT problem directly instead of solving approximate regularized problems, as many state-of-the-art techniques do. This allows us to provide sparse transport plans and avoid numerical issues of methods that use entropic regularization. The algorithm has the same cost per iteration as the popular Sinkhorn method, and each iteration can be executed efficiently, in parallel. The proposed method inherits the strong convergence guarantees of the Douglas-Rachford splitting family. In addition, we establish a linear convergence rate for our formulation of the OT problem. We discuss efficient implementation of the proposed method on GPUs, including how to incorporate stopping criteria without any extra cost. Substantial experiments demonstrate a superior performance of our method, both in terms of computation times and robustness, compared to the state-of-the art.
- One-sentence Summary: We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy.
- Supplementary Material: zip