Cost-augmented Schr\"odinger bridges on graphs are exactly solvable: a Feynman-Kac tilt replaces learned control
Read the original on arXiv Machine Learning →The paper presents a new formulation of the Schr"odinger bridge problem on graphs that incorporates state costs via a Feynman‑Kac tilt, eliminating the need for learned control or temporal‑difference penalties. The resulting cost‑augmented bridge is solved exactly by alternating two endpoint rescalings, each requiring only a sparse matrix‑exponential application, and the method scales linearly with network size. Experiments on a protein‑folding model and a large road‑network demonstrate that the exact bridge reduces expected energy barriers and matches target distributions within sampling error.
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