Nonlocal Mean Field Schrödinger Bridge with Learned Interactions
The Schrödinger Bridge Problem connects an initial distribution to a terminal one along a minimum-energy stochastic process. Its mean-field extension, the Mean-Field Schrödinger Bridge, governs interacting populations whose dynamics and costs depend on the collective distribution. When these interactions are nonlocal, their direct evaluation scales quadratically with the population size, making large ensembles intractable within FBSDE-based solvers. We replace these terms with neural surrogates in state and time, trained on empirical interaction values along sampled trajectories and embedded in a four-stage alternating scheme that updates the forward and backward potentials and the surrog...
| Authors | Daisuke Inoue, Dante Kalise, Mathieu Laurière |
|---|---|
| Primary category | math.OC |
| Published | 2 June 2026 |
| Last updated at source | 2 July 2026 |
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