Title: Deriving Admissible Heuristics Through Cost Partitioning

Abstract: While admissible heuristics are critical for achieving optimal planning, their development is often hindered by the potential for overestimation. Although cost partitioning allows for the combination of multiple abstraction heuristics without sacrificing admissibility, determining optimal partitions in real-time is computationally prohibitive. This paper introduces a novel framework designed to learn the inference of admissible cost partitions, utilizing the Lagrangian dual equivalence that exists between cost partitioning and multiplier prediction. In this approach, planning states and patterns are represented as labeled graphs, and an action-oriented version of the Weisfeiler-Leman algorithm is employed to extract structural feature vectors. These features are then processed by a deep architecture featuring axial self-attention, which feeds into a softmax output layer. This design ensures that the resulting cost weights inherently satisfy partition constraints, thereby guaranteeing admissibility. Experimental results indicate that this method reduces node expansions relative to suboptimal partitioning baselines while upholding strict admissibility. To the best of our knowledge, this represents the first instance of a machine-learned heuristic that is provably admissible.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC