Higher-Dimensional Potential Heuristics for Optimal Classical Planning

TL;DR

This paper extends potential heuristics in classical planning to higher-dimensional features, demonstrating their increased informativeness and analyzing their computational properties through graph-theoretic measures.

Contribution

It generalizes the characterization of potential heuristics to binary features, introduces the context-dependency graph, and explores the complexity of higher-dimensional features.

Findings

Binary potential heuristics are more informative than atomic ones.

The tractability of potential heuristics depends on the treewidth of the context-dependency graph.

Experimental results confirm the effectiveness of binary potential heuristics.

Abstract

Potential heuristics for state-space search are defined as weighted sums over simple state features. Atomic features consider the value of a single state variable in a factored state representation, while binary features consider joint assignments to two state variables. Previous work showed that the set of all admissible and consistent potential heuristics using atomic features can be characterized by a compact set of linear constraints. We generalize this result to binary features and prove a hardness result for features of higher dimension. Furthermore, we prove a tractability result based on the treewidth of a new graphical structure we call the context-dependency graph. Finally, we study the relationship of potential heuristics to transition cost partitioning. Experimental results show that binary potential heuristics are significantly more informative than the previously considered atomic ones.