Cost-augmented Schrödinger bridges on graphs are exactly solvable: a Feynman-Kac tilt replaces learned control
Graph Schrödinger bridges with state costs are solved exactly via a Feynman-Kac tilt, with no learning.
The paper shows that a state cost on a generalized Schrödinger bridge over a graph folds into the reference process as a Feynman-Kac tilt, making the cost-augmented bridge an ordinary bridge against that tilted reference. It is computed exactly by alternating two sparse matrix-exponential endpoint rescalings, without time discretization or learned control. On a protein-folding model a free-energy cost lowers the expected barrier, and road-network rollouts match the target within sampling error with linear memory at millions of intersections.
- A state cost becomes a Feynman-Kac tilt of the reference process.
- The bridge is computed by two sparse matrix-exponential rescalings, with nothing learned.
- Convergence depends only on the endpoint coupling.
- Memory grows linearly on road networks with millions of intersections.
From the original article
1 min read at arxiv.orgThe generalized Schrödinger 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.
By Akshay Balsubramani · arxiv.org
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