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arXiv · 2610.26504

On the Linear Convergence of SISTA for Entropic Martingale Optimal Transport

Giorgia Bifronte·Armand Ley·Maxime Sylvestre
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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 $L^{\infty}$ 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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Giorgia Bifronte, Armand Ley, Maxime Sylvestre. 2026-10-19. On the Linear Convergence of SISTA for Entropic Martingale Optimal Transport. https://arxiv.org/abs/2610.26504

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