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Error estimate for regularized optimal transport problems via Bregman divergence

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arxiv 2309.11666 v2 pith:4FQJGYSI submitted 2023-09-20 math.OC cs.NAmath.NA

Keiichi Morikuni , Koya Sakakibara , Asuka Takatsu This is my paper · ORCID
classification math.OCcs.NAmath.NA
keywords bregmanerrorestimateoptimalproblemsregularizedtransportdivergence
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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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Cited by 1 Pith paper

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  1. Sinkhorn Algorithm for Sequentially Composed Optimal Transports

    cs.DS 2024-12 accept novelty 6.0 of 10

    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.

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