Exponential convergence of Sinkhorn algorithm for entropy martingale optimal transport

Abstract

We prove the exponential convergence in relative entropy of the Sinkhorn algorithm for the entropy martingale optimal transport. We assume that the marginals have compact supports and are in strict convex order, the terminal marginal support is convex, and the initial marginal support lies in the relative interior of the terminal marginal support; the reference cost is assumed to be Lipschitz in each variable. Under these assumptions we establish uniform bounds on the dual variables modulo affine gauges. This result allows us to obtain the existence and uniqueness of the optimizer, and its exponential representation in terms of dual variables. We then establish a relative-entropy stability estimate for martingale couplings with different terminal marginals. Proving that the constant in the stability estimate stays uniform throughout the Sinkhorn iteration allows us to establish the exponential convergence of the Sinkhorn algorithm.

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BibTeX

@misc{kazeykina2026exponential,
  title = {{Exponential convergence of Sinkhorn algorithm for entropy martingale optimal transport}},
  author = {Anna Kazeykina and Zhenjie Ren and Hecheng Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18850},
  eprint = {2609.18850},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18850},
}

RIS

TY  - UNPB
TI  - Exponential convergence of Sinkhorn algorithm for entropy martingale optimal transport
AU  - Anna Kazeykina
AU  - Zhenjie Ren
AU  - Hecheng Wang
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18850
UR  - https://arxiv.org/abs/2609.18850
AB  - We prove the exponential convergence in relative entropy of the Sinkhorn algorithm for the entropy martingale optimal transport. We assume that the marginals have compact supports and are in strict convex order, the terminal marginal support is convex, and the initial marginal support lies in the relative interior of the terminal marginal support; the reference cost is assumed to be Lipschitz in each variable. Under these assumptions we establish uniform bounds on the dual variables modulo affine gauges. This result allows us to obtain the existence and uniqueness of the optimizer, and its exponential representation in terms of dual variables. We then establish a relative-entropy stability estimate for martingale couplings with different terminal marginals. Proving that the constant in the stability estimate stays uniform throughout the Sinkhorn iteration allows us to establish the exponential convergence of the Sinkhorn algorithm.
ER  -

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