Learning Admissible Heuristics via Cost Partitioning

2026-06-03

AI Summary

This work addresses the challenge of efficiently learning admissible heuristic functions without overestimation that leads to suboptimal planning. The authors propose a cost partitioning framework that reformulates the partitioning problem via Lagrangian duality into multiplier prediction. They design a deep neural network with Softmax constraints, integrating label graph encoding, an action-centric Weisfeiler–Leman algorithm, and axial self-attention mechanisms to directly output cost weights that satisfy partitioning constraints. This approach constitutes the first end-to-end method for learning strictly admissible heuristics, where built-in structural constraints guarantee the legality of outputs. Empirically, it significantly reduces the number of expanded search nodes while rigorously preserving admissibility.

Abstract

Admissible heuristics are essential for optimal planning, yet learning them remains challenging due to the risk of overestimation. Cost partitioning combines multiple abstraction heuristics while preserving admissibility, but computing optimal partitions online is expensive. We propose a framework that learns to infer admissible cost partitions by leveraging the Lagrangian dual equivalence between cost partitioning and multiplier prediction. Planning states and patterns are encoded as labelled graphs, and an action-centric variant of the Weisfeiler-Leman algorithm extracts structural feature vectors. A deep architecture with axial self-attention and a softmax output layer maps these features to cost weights that satisfy the partition constraints by construction, ensuring admissibility. Experiments demonstrate reduced node expansions compared to suboptimal partitioning baselines while maintaining strict admissibility. To our knowledge, this is the first machine-learned heuristic guaranteed to be admissible.

Problem

• admissible heuristics
• cost partitioning
• optimal planning
• overestimation
• heuristic learning

Innovation

• admissible heuristics
• cost partitioning
• Lagrangian dual
• Weisfeiler-Leman algorithm
• axial self-attention