Learning Shortest Paths with Generative Flow Networks
This addresses pathfinding challenges in AI and optimization, offering a novel learning-based method with incremental improvements over specialized approaches.
The paper tackles the problem of finding shortest paths in graphs by using Generative Flow Networks (GFlowNets), proving that minimizing total flow ensures traversal along shortest paths and demonstrating competitive results in solving Rubik's Cubes with smaller search budgets.
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.