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arxiv: 2606.02438 · v1 · pith:MAUM2I7Unew · submitted 2026-06-01 · 💻 cs.AI

LLM-Evolved Pattern Generators for Optimal Classical Planning

Windy Phung , Dominik Drexler , Arnaud Lequen , Jendrik Seipp This is my paper

Pith reviewed 2026-06-28 14:10 UTC · model grok-4.3

classification 💻 cs.AI
keywords classical planningadmissible heuristicspattern collectionssaturated cost partitioningLLM program synthesisevolutionary searchoptimal planningA* search
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The pith

LLM-evolved programs generate pattern collections that induce admissible heuristics matching baseline coverage while evaluating states faster.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the first method to learn domain-dependent heuristics for optimal classical planning that remain admissible by construction. Rather than training a direct state-to-value mapping, it evolves programs that output pattern collections for any task in a given domain. These collections are combined with saturated cost partitioning to guarantee admissibility and thus preserve A* optimality. The programs are discovered by an evolutionary synthesis loop driven by a large language model. When the approach succeeds, the resulting heuristics achieve the same coverage as strong domain-independent baselines on several domains but incur substantially lower evaluation cost per state.

Core claim

The central claim is that an LLM-driven evolutionary program-synthesis framework can produce, for each planning domain, a program that outputs a pattern collection for any task in that domain; when the resulting patterns are combined admissibly via saturated cost partitioning, the induced heuristics match the coverage of state-of-the-art domain-independent baselines while evaluating each state substantially faster and preserving optimality guarantees.

What carries the argument

An LLM-driven evolutionary program-synthesis framework that evolves programs producing pattern collections, which are then combined via saturated cost partitioning to form admissible heuristics.

If this is right

  • The learned programs encode interpretable domain-specific insights.
  • The heuristics incur negligible overhead at test time.
  • They match the coverage of state-of-the-art domain-independent baselines on several domains.
  • Each state is evaluated substantially faster than with the baselines.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same synthesis loop could be applied to other search settings that require admissible estimates, such as certain scheduling or verification tasks.
  • Because the programs are explicit, they might be inspected or edited by humans to inject additional domain knowledge.
  • Success on more domains would reduce dependence on hand-engineered domain-independent heuristics in planning systems.
  • Failure on a domain would point to limits in the current evolutionary operators or prompt design rather than in the admissibility guarantee itself.

Load-bearing premise

An LLM-driven evolutionary program-synthesis framework can reliably obtain, for each domain, a program that produces a pattern collection yielding competitive admissible heuristics.

What would settle it

Finding even one domain where the evolved programs produce heuristics with lower coverage than the baselines or that return non-admissible values on some tasks would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.02438 by Arnaud Lequen, Dominik Drexler, Jendrik Seipp, Windy Phung.

Figure 1
Figure 1. Figure 1: One iteration of OpenEvolve. Each island [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The evolutionary pipeline. The engine (blue) cre [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Combined score per iteration for all domains. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Total search time: h evo vs. each baseline. Points below the diagonal indicate tasks where h evo is faster. 4.3 Example Pattern Collection Generators In this section, we describe pattern collection generators synthesized for three representative domains and analyze their empirical behavior in more depth. Childsnack. In Childsnack, sandwiches must be assem￾bled and delivered to children waiting at tables, s… view at source ↗
Figure 6
Figure 6. Figure 6: Time per heuristic evaluation: h evo vs. each base￾line. Points below the diagonal indicate tasks where h evo evaluates each state more cheaply. their destination floors. Our generator produces three pat￾tern types: singleton state atoms (boarded or served, 1 atom each); lift floor patterns grouping lift-at atoms for adjacent or globally relevant floor pairs (1–19 atoms); and per-passenger journey patterns… view at source ↗
read the original abstract

Learned heuristics have recently become a competitive alternative to traditional domain-independent heuristics for satisficing planning. Existing approaches, however, focus on improving search guidance rather than guaranteeing admissibility, which makes them unsuitable for optimal classical planning. We present the first method for learning domain-dependent heuristics that are admissible by design and thus preserve the optimality guarantees of A* search. Instead of learning a direct mapping from states to heuristic values, we learn to construct abstractions that induce admissible heuristics. We use an LLM-driven evolutionary program-synthesis framework to obtain, for each domain, a program that produces a pattern collection for any task in that domain, and we combine the resulting patterns admissibly via saturated cost partitioning. Empirically, the learned programs encode interpretable domain-specific insights, run with negligible overhead at test time and yield heuristics that match the coverage of state-of-the-art domain-independent baselines on several domains while evaluating each state substantially faster.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims to introduce the first method for learning domain-dependent admissible heuristics for optimal classical planning. Instead of directly learning state-to-value mappings, it uses an LLM-driven evolutionary program-synthesis framework to discover, per planning domain, a program that generates a pattern collection for any task in that domain; the resulting patterns are then combined admissibly via saturated cost partitioning to yield a heuristic that preserves A* optimality. The abstract reports that the learned programs are interpretable, incur negligible test-time overhead, match the coverage of state-of-the-art domain-independent baselines on several domains, and evaluate states substantially faster.

Significance. If the empirical claims are substantiated, the work would be significant: it demonstrates a route to domain-dependent admissible heuristics that retain optimality guarantees while incorporating learned, interpretable structure. The evolutionary synthesis approach for generating pattern-collection programs is a distinctive technical contribution that could be extended beyond planning.

major comments (2)
  1. [Experiments] Experiments section: the manuscript states that the learned heuristics 'match the coverage of state-of-the-art domain-independent baselines on several domains while evaluating each state substantially faster,' yet supplies no description of the experimental protocol (domains, instance counts, number of independent runs, statistical tests for coverage or runtime differences, or failure modes). This information is load-bearing for assessing the central empirical claim.
  2. [Method] Method section: while admissibility of the final heuristic follows from the standard properties of pattern databases and saturated cost partitioning, the paper provides no formal argument or pseudocode establishing that the evolutionary search is guaranteed to terminate with a program that produces valid (i.e., well-formed) pattern collections for every task in the target domain.
minor comments (2)
  1. [Introduction] The abstract and introduction repeatedly use the phrase 'first method' without a precise comparison table or citation list that distinguishes the new contribution from prior work on learned admissible heuristics or evolutionary program synthesis in planning.
  2. [Method] Notation for the evolutionary fitness function and the saturated-cost-partitioning combination step is introduced without an explicit equation or algorithm listing, making it difficult to verify reproducibility from the text alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below.

read point-by-point responses

  1. Referee: [Experiments] Experiments section: the manuscript states that the learned heuristics 'match the coverage of state-of-the-art domain-independent baselines on several domains while evaluating each state substantially faster,' yet supplies no description of the experimental protocol (domains, instance counts, number of independent runs, statistical tests for coverage or runtime differences, or failure modes). This information is load-bearing for assessing the central empirical claim.

    Authors: We agree that the current manuscript lacks a sufficient description of the experimental protocol. In the revision we will add a dedicated subsection detailing the domains and instance counts, the number of independent runs, the statistical tests applied to coverage and runtime results, and any observed failure modes. revision: yes

  2. Referee: [Method] Method section: while admissibility of the final heuristic follows from the standard properties of pattern databases and saturated cost partitioning, the paper provides no formal argument or pseudocode establishing that the evolutionary search is guaranteed to terminate with a program that produces valid (i.e., well-formed) pattern collections for every task in the target domain.

    Authors: The evolutionary procedure is stochastic and LLM-driven, so it does not admit a formal termination guarantee that every generated program will be valid. We will nevertheless add pseudocode for the full evolutionary loop together with a description of the validation and rejection steps that discard malformed programs. This clarifies the practical safeguards without claiming an absolute guarantee. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's core derivation is that LLM-evolved programs generate pattern collections whose induced heuristics remain admissible because (a) projections preserve admissibility (standard PDB property) and (b) saturated cost partitioning preserves admissibility (standard operator). These properties are invoked from the planning literature rather than derived inside the paper or via self-citation chains. The evolutionary synthesis step is presented only as a discovery procedure whose output is then evaluated empirically on coverage and runtime; no equation defines a fitted parameter that is later renamed a prediction, and no uniqueness theorem or ansatz is smuggled in. The reported results are therefore falsifiable external measurements rather than algebraic identities of the method's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard planning assumption that saturated cost partitioning of pattern collections yields admissible heuristics, plus the unverified premise that evolutionary search over LLM-generated programs will discover effective domain-specific generators.

axioms (1)
  • domain assumption Saturated cost partitioning of multiple pattern databases produces an admissible heuristic.
    This is a standard result in classical planning literature invoked to guarantee admissibility.

pith-pipeline@v0.9.1-grok · 5688 in / 1164 out tokens · 30129 ms · 2026-06-28T14:10:18.760237+00:00 · methodology

discussion (0)

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