Learning Shortest Paths with Generative Flow Networks

2026-03-02

AI Summary

This work reframes the shortest path problem as a generative flow network (GFlowNet) learning task, where the policy is trained to traverse only along shortest paths by minimizing a total flow constraint. It presents the first extension of GFlowNet theory to non-acyclic graph environments and proves that, under this formulation, the model can exactly generate shortest paths. The approach introduces a novel paradigm for learning optimal paths without explicit search, leveraging flow regularization and joint modeling of forward and backward policies. Empirical validation on combinatorial permutation and 3×3×3 Rubik’s Cube solving tasks demonstrates that the method achieves path lengths comparable to specialized state-of-the-art solvers while requiring significantly less search budget at test time.

Technology Category

• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

In this paper, we present a novel learning framework for finding shortest paths in graphs utilizing Generative Flow Networks (GFlowNets). First, we examine theoretical properties of GFlowNets in non-acyclic environments in relation to shortest paths. We prove that, if the total flow is minimized, forward and backward policies traverse the environment graph exclusively along shortest paths between the initial and terminal states. Building on this result, we show that the pathfinding problem in an arbitrary graph can be solved by training a non-acyclic GFlowNet with flow regularization. We experimentally demonstrate the performance of our method in pathfinding in permutation environments and in solving Rubik's Cubes. For the latter problem, our approach shows competitive results with state-of-the-art machine learning approaches designed specifically for this task in terms of the solution length, while requiring smaller search budget at test-time.

Problem

• shortest paths
• graph
• pathfinding
• non-acyclic environments
• Rubik's Cube

Innovation

• Generative Flow Networks
• shortest path
• non-acyclic graphs
• flow regularization
• pathfinding