# Schrodinger Bridge over Averaged Systems

arXiv: https://arxiv.org/abs/2412.03294 · HTML: https://mlsanity.com/paper/2412.03294/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2024.

## Built on by (most cited first, 1 of 1)

- [Lifted Schr"odinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions](https://mlsanity.com/paper/2605.24795/) (2026)

## Abstract (arXiv)

We consider a Schr"odinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using controls robust to the parameter perturbations. Utilizing the path integral formalism, we demonstrate that the optimal control is a non-Markovian strategy, specifically a stochastic feedforward control, which depends on past and present noise. This unexpected deviation from established strategies for Schr"odinger bridge problems highlights the intricate interrelationships present in the system's dynamics. From the perspective of optimal transport, a significant by-product of our work is the demonstration that, when the evolution of a distribution is subject to parameter perturbations, it is possible to robustly deform the distribution to a desired final state using stochastic feedforward controls.