# Graph Learning for Numeric Planning

arXiv: https://arxiv.org/abs/2410.24080 · HTML: https://mlsanity.com/paper/2410.24080/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 78 references that are in the map.
- First posted on arXiv 31 Oct 2024.

## Builds on (most cited first, 30 of 33)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Reward Machines: Exploiting Reward Function Structure in Reinforcement Learning](https://mlsanity.com/paper/2010.03950/) (2020)
- [Generalized Planning in PDDL Domains with Pretrained Large Language Models](https://mlsanity.com/paper/2305.11014/) (2023)
- [Wasserstein Weisfeiler-Lehman Graph Kernels](https://mlsanity.com/paper/1906.01277/) (2019)
- [Learning Domain-Independent Planning Heuristics with Hypergraph Networks](https://mlsanity.com/paper/1911.13101/) (2019)
- [Predicate Invention for Bilevel Planning](https://mlsanity.com/paper/2203.09634/) (2022)
- [ASNets: Deep Learning for Generalised Planning](https://mlsanity.com/paper/1908.01362/) (2019)
- [Planning with Learned Object Importance in Large Problem Instances using Graph Neural Networks](https://mlsanity.com/paper/2009.05613/) (2020)
- [Learning General Optimal Policies with Graph Neural Networks: Expressive Power, Transparency, and Limits](https://mlsanity.com/paper/2109.10129/) (2021)
- [Faster Kernels for Graphs with Continuous Attributes via Hashing](https://mlsanity.com/paper/1610.00064/) (2016)
- [Learning Domain-Independent Heuristics for Grounded and Lifted Planning](https://mlsanity.com/paper/2312.11143/) (2023)
- [Features, Projections, and Representation Change for Generalized Planning](https://mlsanity.com/paper/1801.10055/) (2018)
- [Learning to Rank for Synthesizing Planning Heuristics](https://mlsanity.com/paper/1608.01302/) (2016)
- [Learning Generalized Relational Heuristic Networks for Model-Agnostic Planning](https://mlsanity.com/paper/2007.06702/) (2020)
- [Reinforcement Learning for Classical Planning: Viewing Heuristics as Dense Reward Generators](https://mlsanity.com/paper/2109.14830/) (2021)
- [Return to Tradition: Learning Reliable Heuristics with Classical Machine Learning](https://mlsanity.com/paper/2403.16508/) (2024)
- [Qualitative Numeric Planning: Reductions and Complexity](https://mlsanity.com/paper/1912.04816/) (2019)
- [Generalized Planning as Heuristic Search](https://mlsanity.com/paper/2103.14434/) (2021)
- [DANLI: Deliberative Agent for Following Natural Language Instructions](https://mlsanity.com/paper/2210.12485/) (2022)
- [Model-free, Model-based, and General Intelligence](https://mlsanity.com/paper/1806.02308/) (2018)
- [Scaling-up Generalized Planning as Heuristic Search with Landmarks](https://mlsanity.com/paper/2205.04850/) (2022)
- [Online Planner Selection with Graph Neural Networks and Adaptive Scheduling](https://mlsanity.com/paper/1811.00210/) (2018)
- [Optimize Planning Heuristics to Rank, not to Estimate Cost-to-Goal](https://mlsanity.com/paper/2310.19463/) (2023)
- [What Planning Problems Can A Relational Neural Network Solve?](https://mlsanity.com/paper/2312.03682/) (2023)
- [Egocentric Planning for Scalable Embodied Task Achievement](https://mlsanity.com/paper/2306.01295/) (2023)
- [Novelty Heuristics, Multi-Queue Search, and Portfolios for Numeric Planning](https://mlsanity.com/paper/2404.05235/) (2024)
- [Hierarchical Decomposition and Analysis for Generalized Planning](https://mlsanity.com/paper/2212.02823/) (2022)
- [Online Grounding of Symbolic Planning Domains in Unknown Environments](https://mlsanity.com/paper/2112.10007/) (2021)

## Built on by (most cited first, 5 of 5)

- [Weisfeiler-Leman Features for Planning: A 1,000,000 Sample Size Hyperparameter Study](https://mlsanity.com/paper/2508.18515/) (2025)
- [Vejde: A Framework for Inductive Deep Reinforcement Learning Based on Factor Graph Color Refinement](https://mlsanity.com/paper/2509.09219/) (2025)
- [Graph Learning for Planning: The Story Thus Far and Open Challenges](https://mlsanity.com/paper/2412.02136/) (2024)
- [Learning to Search and Searching to Learn for Generalization in Planning](https://mlsanity.com/paper/2605.25720/) (2026)
- [Neuro-Symbolic Learning for Long-Horizon Task Planning Under Complex Logical Constraints](https://mlsanity.com/paper/2606.06877/) (2026)

## Abstract (arXiv)

Graph learning is naturally well suited for use in symbolic, object-centric planning due to its ability to exploit relational structures exhibited in planning domains and to take as input planning instances with arbitrary numbers of objects. Numeric planning is an extension of symbolic planning in which states may now also exhibit numeric variables. In this work, we propose data-efficient and interpretable machine learning models for learning to solve numeric planning tasks. This involves constructing a new graph kernel for graphs with both continuous and categorical attributes, as well as new optimisation methods for learning heuristic functions for numeric planning. Experiments show that our graph kernels are vastly more efficient and generalise better than graph neural networks for numeric planning, and also yield competitive coverage performance compared to domain-independent numeric planners. Code is available at https://github.com/DillonZChen/goose