mlsanityData to 14 Oct 2026

A Generalized Sinkhorn Algorithm for Mean-Field Schr"odinger Bridge

arXiv 2604.06531 ↗First posted 8 Apr 2026math.OC cs.LG cs.MAcited by 3

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Abstract (arXiv)

The mean-field Schr"odinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline. Unlike the standard Schr"odinger bridge, the dynamical constraint for MFSB is the mean-field limit of a population of interacting agents with controls. It serves as a natural model for large-scale multi-agent systems. The MFSB is computationally challenging because the nonlocal interaction makes the problem nonconvex. We propose a generalization of the Hopf-Cole transform for MFSB and, building on it, design a Sinkhorn-type recursive algorithm to solve the associated system of integro-PDEs. Under mild assumptions on the interaction potential, we discuss convergence guarantees for the proposed algorithm. We present numerical examples with repulsive and attractive interactions to illustrate the theoretical contributions.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 14 of its 34 references that are in the map. First posted on arXiv 8 Apr 2026.

Builds on

14 of 34 references.

References · 14

  1. 2019Wasserstein Proximal Algorithms for the Schr"odinger Bridge Problem: Density Control with Nonlinear Driftcited by 50
  2. 2015Entropic and displacement interpolation: a computational approach using the Hilbert metriccited by 34
  3. 2020Reflected Schr"odinger Bridge: Density Control with Path Constraintscited by 22
  4. 2014Optimal steering of a linear stochastic system to a final probability distribution, part IIcited by 17
  5. 2021Density control of interacting agent systemscited by 13
  6. 2016Optimal steering of a linear stochastic system to a final probability distribution, Part IIIcited by 12
  7. 2024Schr"odinger Bridge with Quadratic State Cost is Exactly Solvablecited by 12
  8. 2019Finite Horizon Density Steering for Multi-input State Feedback Linearizable Systemscited by 11
  9. 2023Neural Schr"odinger Bridge with Sinkhorn Losses: Application to Data-driven Minimum Effort Control of Colloidal Self-assemblycited by 10
  10. 2023Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithmcited by 8
  11. 2025On the Hopf-Cole Transform for Control-affine Schr"odinger Bridgecited by 5
  12. 2023Schr"odinger's control and estimation paradigm with spatio-temporal distributions on graphscited by 4
2 more
  1. 2024An excursion onto Schr"odinger's bridges: Stochastic flows with spatio-temporal marginalscited by 3
  2. 2025Markov Kernels, Distances and Optimal Control: A Parable of Linear Quadratic Non-Gaussian Distribution Steeringcited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Nonlocal Mean Field Schr"odinger Bridge with Learned Interactionscited by 1
  2. 2026Schr"odinger Bridges over Kinetic Swarming Modelscited by 0
  3. 2026Cost-augmented Schr"odinger bridges on graphs are exactly solvable: a Feynman-Kac tilt replaces learned controlcited by 0