A Sinkhorn-Newton method for entropic optimal transport
This work addresses computational efficiency in optimal transport for applications like machine learning and imaging, but it is incremental as it builds on existing methods with specific improvements.
The authors tackled the problem of solving entropic optimal transport by proposing a Sinkhorn-Newton method, which achieves quadratic convergence and outperforms the Sinkhorn-Knopp algorithm for small regularization strengths, as validated numerically.
We consider the entropic regularization of discretized optimal transport and propose to solve its optimality conditions via a logarithmic Newton iteration. We show a quadratic convergence rate and validate numerically that the method compares favorably with the more commonly used Sinkhorn--Knopp algorithm for small regularization strength. We further investigate numerically the robustness of the proposed method with respect to parameters such as the mesh size of the discretization.