Cost-augmented Schr\"odinger bridges on graphs are exactly solvable: a Feynman-Kac tilt replaces learned control

Excerpt

arXiv:2610.02195v1 Announce Type: new Abstract: The generalized Schr\"odinger bridge on a graph moves mass between two distributions while charging a cost for the states visited. It has been approached by learning the rates of a controlled continuous-time Markov chain, with a temporal-difference penalty that restores the cost. A state cost folds into the reference process as a Feynman-Kac tilt. The cost-augmented bridge is then a plain bridge against the tilted reference, and the penalty is unne