Cost-augmented optimal transport on graphs can be solved exactly and efficiently using matrix exponentials instead of learned neural networks—no approximation or temporal discretization needed.
This paper solves the cost-augmented Schrödinger bridge problem on graphs exactly, without learning or time discretization. By reformulating state costs as a Feynman-Kac tilt of the reference process, the problem reduces to computing a standard bridge through alternating matrix exponentials. The method is exact, memory-efficient, and converges based on endpoint coupling alone.