Generalized Schr\"odinger Bridge on Graphs

TL;DR

This paper introduces GSBoG, a scalable, data-driven framework for learning control policies on graphs that respect topology and optimize costs, overcoming limitations of previous methods.

Contribution

GSBoG is a novel framework that learns trajectory-level policies on arbitrary graphs using likelihood optimization, improving scalability and expressivity.

Findings

GSBoG accurately learns topology-respecting policies.

It effectively optimizes intermediate state costs.

The method scales well to large, real-world graphs.

Abstract

Transportation on graphs is a fundamental challenge across many domains, where decisions must respect topological and operational constraints. Despite the need for actionable policies, existing graph-transport methods lack this expressivity. They rely on restrictive assumptions, fail to generalize across sparse topologies, and scale poorly with graph size and time horizon. To address these issues, we introduce Generalized Schr\"odinger Bridge on Graphs (GSBoG), a novel scalable data-driven framework for learning executable controlled continuous-time Markov chain (CTMC) policies on arbitrary graphs under state cost augmented dynamics. Notably, GSBoG learns trajectory-level policies, avoiding dense global solvers and thereby enhancing scalability. This is achieved via a likelihood optimization approach, satisfying the endpoint marginals, while simultaneously optimizing intermediate behavior under state-dependent running costs. Extensive experimentation on challenging real-world graph topologies shows that GSBoG reliably learns accurate, topology-respecting policies while optimizing application-specific intermediate state costs, highlighting its broad applicability and paving new avenues for cost-aware dynamical transport on general graphs.