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PreprintCC BY 4.0arXiv

Initialization Stability and Convergence of Projected Langevin Dynamics

  • Qi Feng
  • Nathan Sauldubois
  • Xin Zhang
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Abstract

The entropic regularized optimal transport (EOT) plays a fundamental role in the computation of optimal transport. In \cite{CLP}, the authors proposed a gradient flow approach to EOT, and derived a projected Langevin diffusion that converges in distribution to the solution of EOT when initialized with a coupling between the two given marginals. In this paper, motivated by samplings of optimal couplings for EOT, we analyze the projected Langevin dynamics with arbitrary initial distribution, and prove that its long time behavior is the same as if it was initialized from a coupling.

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Cite

BibTeXRIS
BibTeX
@misc{feng2026initialization,
  title = {{Initialization Stability and Convergence of Projected Langevin Dynamics}},
  author = {Qi Feng and Nathan Sauldubois and Xin Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35369},
  eprint = {2610.35369},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35369},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Initialization Stability and Convergence of Projected Langevin Dynamics
AU  - Qi Feng
AU  - Nathan Sauldubois
AU  - Xin Zhang
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35369
UR  - https://arxiv.org/abs/2610.35369
AB  - The entropic regularized optimal transport (EOT) plays a fundamental role in the computation of optimal transport. In \cite{CLP}, the authors proposed a gradient flow approach to EOT, and derived a projected Langevin diffusion that converges in distribution to the solution of EOT when initialized with a coupling between the two given marginals. In this paper, motivated by samplings of optimal couplings for EOT, we analyze the projected Langevin dynamics with arbitrary initial distribution, and prove that its long time behavior is the same as if it was initialized from a coupling.
ER  -