A Sinkhorn-type algorithm for sequentially composed optimal transport is shown to converge exponentially in the Hilbert metric and, for two stages, to have near-linear worst-case time in the plan size.
Error estimate for regularized optimal transport problems via Bregman divergence
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abstract
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the required properties for Bregman divergences, provide a non-asymptotic error estimate for the regularized problem, and show that the error estimate becomes faster than exponentially.
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Sinkhorn Algorithm for Sequentially Composed Optimal Transports
A Sinkhorn-type algorithm for sequentially composed optimal transport is shown to converge exponentially in the Hilbert metric and, for two stages, to have near-linear worst-case time in the plan size.