CONVERGENCE RATES FOR DISTRIBUTION MATCHING WITH SLICED OPTIMAL TRANSPORT

Gauthier Thurin, Claire Boyer, Kimia Nadjahi
Proceedings of Thirty Ninth Conference on Learning Theory, PMLR 336:6156-6196, 2026.

Abstract

We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport. We investigate convergence to the target distribution and derive quantitative non-asymptotic rates. To this end, we establish Lojasiewicz-type inequalities for the Sliced-Wasserstein objective. A key challenge is to control along the trajectory the constants in these inequalities. We show that this becomes tractable for Gaussian distributions. Specifically, eigenvalues are controlled when matching along random orthonormal bases at each iteration. We complement our theory with numerical experiments and illustrate the predicted dependence on dimension and step-size, as well as the stabilizing effect of orthonormal-basis sampling.

Cite this Paper

BibTeX
@InProceedings{pmlr-v336-thurin26a, title = {CONVERGENCE RATES FOR DISTRIBUTION MATCHING WITH SLICED OPTIMAL TRANSPORT}, author = {Thurin, Gauthier and Boyer, Claire and Nadjahi, Kimia}, booktitle = {Proceedings of Thirty Ninth Conference on Learning Theory}, pages = {6156--6196}, year = {2026}, editor = {Hanneke, Steve and Lattimore, Tor}, volume = {336}, series = {Proceedings of Machine Learning Research}, month = {29 Jun--03 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v336/main/assets/thurin26a/thurin26a.pdf}, url = {https://proceedings.mlr.press/v336/thurin26a.html}, abstract = { We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport. We investigate convergence to the target distribution and derive quantitative non-asymptotic rates. To this end, we establish Lojasiewicz-type inequalities for the Sliced-Wasserstein objective. A key challenge is to control along the trajectory the constants in these inequalities. We show that this becomes tractable for Gaussian distributions. Specifically, eigenvalues are controlled when matching along random orthonormal bases at each iteration. We complement our theory with numerical experiments and illustrate the predicted dependence on dimension and step-size, as well as the stabilizing effect of orthonormal-basis sampling.} }
Endnote
%0 Conference Paper %T CONVERGENCE RATES FOR DISTRIBUTION MATCHING WITH SLICED OPTIMAL TRANSPORT %A Gauthier Thurin %A Claire Boyer %A Kimia Nadjahi %B Proceedings of Thirty Ninth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2026 %E Steve Hanneke %E Tor Lattimore %F pmlr-v336-thurin26a %I PMLR %P 6156--6196 %U https://proceedings.mlr.press/v336/thurin26a.html %V 336 %X We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport. We investigate convergence to the target distribution and derive quantitative non-asymptotic rates. To this end, we establish Lojasiewicz-type inequalities for the Sliced-Wasserstein objective. A key challenge is to control along the trajectory the constants in these inequalities. We show that this becomes tractable for Gaussian distributions. Specifically, eigenvalues are controlled when matching along random orthonormal bases at each iteration. We complement our theory with numerical experiments and illustrate the predicted dependence on dimension and step-size, as well as the stabilizing effect of orthonormal-basis sampling.
APA
Thurin, G., Boyer, C. & Nadjahi, K.. (2026). CONVERGENCE RATES FOR DISTRIBUTION MATCHING WITH SLICED OPTIMAL TRANSPORT. Proceedings of Thirty Ninth Conference on Learning Theory, in Proceedings of Machine Learning Research 336:6156-6196 Available from https://proceedings.mlr.press/v336/thurin26a.html.

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