# Relaxed Schroedinger bridges and robust network routing

arXiv: https://arxiv.org/abs/1801.07852 · HTML: https://mlsanity.com/paper/1801.07852/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2018.

## Built on by (most cited first, 2 of 2)

- [Soft-constrained Schrodinger Bridge: a Stochastic Control Approach](https://mlsanity.com/paper/2403.01717/) (2024)
- [The Risk-Sensitive Schr"odinger Bridge: Is Not a KL Projection](https://mlsanity.com/paper/2609.27250/) (2026)

## Abstract (arXiv)

We consider network routing under random link failures with a desired final distribution. We provide a mathematical formulation of a relaxed transport problem where the final distribution only needs to be close to the desired one. The problem is a maximum entropy problem for path distributions with an extra terminal cost. We show that the unique solution may be obtained solving a generalized Schroedinger system. An iterative algorithm to compute the solution is provided. It contracts the Hilbert metric with contraction ratio less than 1/2 leading to extremely fast convergence.