# LeanPlan: Optimal Planning with LLM-Generated Heuristics and Admissibility Proofs

arXiv: https://arxiv.org/abs/2610.08246 · HTML: https://mlsanity.com/paper/2610.08246/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 73 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 5 of 5)

- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [Frontier Large Language Models Rival State-of-the-Art Planners](https://mlsanity.com/paper/2511.09378/) (2025)
- [P3: Joint Program-and-Proof Planning for Verified Code Generation](https://mlsanity.com/paper/2608.09277/) (2026)

## Abstract (arXiv)

Frontier large language models (LLMs) can generate heuristic functions that guide search to achieve state-of-the-art performance in satisficing planning, where any plan is acceptable. However, these heuristics are not guaranteed to be admissible and can lead to suboptimal plans. We introduce LeanPlan, the first planning system that finds optimal plans with LLM-generated heuristics whose admissibility is machine-checked. Given a domain description and training tasks, an agentic loop uses planner feedback to iteratively improve a reusable domain-specific heuristic, its admissibility proof and the required domain assumptions. LeanPlan implements the heuristic, its proof and an efficient planner with machine-checked grounding and search in Lean 4. We evaluate LeanPlan on ten domains from the International Planning Competition and three new domains, using test tasks with up to 57 times as many objects as the training tasks. With GPT-5.6 Sol in the agentic loop, we successfully generate heuristics and admissibility proofs for all these domains. With the resulting heuristics, LeanPlan usually expands fewer states than the state-of-the-art Scorpion planner and solves more tasks overall.