Learning Shortest Paths with Generative Flow Networks

TL;DR

This paper introduces a new framework using Generative Flow Networks to efficiently find shortest paths in graphs, with theoretical guarantees and practical success in complex environments like Rubik's Cubes.

Contribution

It provides the first theoretical analysis of GFlowNets for shortest path problems and demonstrates their effectiveness in complex, non-acyclic environments.

Findings

Theoretical proof that flow-minimized GFlowNets traverse shortest paths.

Successful application to permutation environments and Rubik's Cube.

Competitive solution lengths with reduced search at test-time.

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.