# Learning Admissible Heuristics via Cost Partitioning

arXiv: https://arxiv.org/abs/2606.04597 · HTML: https://mlsanity.com/paper/2606.04597/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Axial Attention in Multidimensional Transformers](https://mlsanity.com/paper/1912.12180/) (2019)
- [Learning Domain-Independent Planning Heuristics with Hypergraph Networks](https://mlsanity.com/paper/1911.13101/) (2019)
- [ASNets: Deep Learning for Generalised Planning](https://mlsanity.com/paper/1908.01362/) (2019)
- [Learning General Optimal Policies with Graph Neural Networks: Expressive Power, Transparency, and Limits](https://mlsanity.com/paper/2109.10129/) (2021)
- [Learning Domain-Independent Heuristics for Grounded and Lifted Planning](https://mlsanity.com/paper/2312.11143/) (2023)
- [Learning to Rank for Synthesizing Planning Heuristics](https://mlsanity.com/paper/1608.01302/) (2016)
- [Learning Generalized Policies Without Supervision Using GNNs](https://mlsanity.com/paper/2205.06002/) (2022)
- [Return to Tradition: Learning Reliable Heuristics with Classical Machine Learning](https://mlsanity.com/paper/2403.16508/) (2024)
- [Classical Planning with LLM-Generated Heuristics: Challenging the State of the Art with Python Code](https://mlsanity.com/paper/2503.18809/) (2025)
- [Language Models For Generalised PDDL Planning: Synthesising Sound and Programmatic Policies](https://mlsanity.com/paper/2508.18507/) (2025)
- [Leveraging Action Relational Structures for Integrated Learning and Planning](https://mlsanity.com/paper/2504.20318/) (2025)

## Abstract (arXiv)

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.