On the Linear Convergence of SISTA for Entropic Martingale Optimal Transport
Abstract
We prove a linear convergence rate of a Sinkhorn-type algorithm for entropic martingale optimal transport in arbitrary dimension. The algorithm follows a block-coordinate ascent scheme, alternating exact Sinkhorn updates for the marginal potentials with an explicit gradient step for the potential associated with the martingale constraint. Under irreducibility and non-degeneracy assumptions on the compactly supported marginals, we establish linear convergence of the dual objective values and iterates. Our analysis relies on a pointwise coercivity estimate involving the gradient of the dual functional with respect to the potential for the martingale constraint. This property allows us to establish uniform L∞ bounds on the iterates. Combining these bounds with smoothness and strong convexity modulo affine invariances yields a uniform Polyak--Łojasiewicz inequality along the iterations and, consequently, a linear convergence rate. We complement our theoretical results with numerical experiments illustrating the convergence behavior of the algorithm.
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BibTeX
@misc{bifronte2026linear,
title = {{On the Linear Convergence of SISTA for Entropic Martingale Optimal Transport}},
author = {Giorgia Bifronte and Armand Ley and Maxime Sylvestre},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26504},
eprint = {2610.26504},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26504},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Linear Convergence of SISTA for Entropic Martingale Optimal Transport
AU - Giorgia Bifronte
AU - Armand Ley
AU - Maxime Sylvestre
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26504
UR - https://arxiv.org/abs/2610.26504
AB - We prove a linear convergence rate of a Sinkhorn-type algorithm for entropic martingale optimal transport in arbitrary dimension. The algorithm follows a block-coordinate ascent scheme, alternating exact Sinkhorn updates for the marginal potentials with an explicit gradient step for the potential associated with the martingale constraint. Under irreducibility and non-degeneracy assumptions on the compactly supported marginals, we establish linear convergence of the dual objective values and iterates. Our analysis relies on a pointwise coercivity estimate involving the gradient of the dual functional with respect to the potential for the martingale constraint. This property allows us to establish uniform L^∞ bounds on the iterates. Combining these bounds with smoothness and strong convexity modulo affine invariances yields a uniform Polyak--Łojasiewicz inequality along the iterations and, consequently, a linear convergence rate. We complement our theoretical results with numerical experiments illustrating the convergence behavior of the algorithm.
ER -