Learning Heuristic Functions with Graph Neural Networks for Numeric Planning

In this paper, we investigate the application of heuristics based on Graph Neural Networks (GNNs) to lifted numeric planning problems, an area that has been relatively unexplored. Building upon the GNN approach for learning general policies proposed by Ståhlberg, Bonet, and Geffner (2022b), we extend the architecture to make it sensitive to the numeric components inherent in the planning problems we address. We achieve this by observing that, although the state space of a numeric planning problem is infinite, the finite subgoal structure of the problem can be incorporated into the architecture, enabling the construction of a finite structure. Instead of learning general policies, we train our models to serve as heuristics within a best-first search algorithm. We explore various configurations of this architecture and demonstrate that the resulting heuristics are highly informative and, in certain domains, offer a better trade-off between guidance and computational cost compared to state-of-the-art heuristics.