arxiv: 2604.15709 · v1 · submitted 2026-04-17 · 💻 cs.AI

Recognition: unknown

Bilevel Optimization of Agent Skills via Monte Carlo Tree Search

Chenyi Huang , Haoting Zhang , Jingxu Xu , Zeyu Zheng , Yunduan Lin

Authors on Pith no claims yet

Pith reviewed 2026-05-10 09:11 UTC · model grok-4.3

classification 💻 cs.AI

keywords bilevel optimizationMonte Carlo Tree SearchLLM agentsskill optimizationskill structurecontent refinementoperations research question answering

0 comments

The pith

Bilevel optimization separates skill structure search from content refinement to improve LLM agent performance.

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

The paper aims to establish that skills for large language model agents can be optimized by casting their design as a bilevel problem. An outer loop applies Monte Carlo Tree Search to select structures of instructions, tools, and resources, while an inner loop uses LLMs to adjust the content within each structure. A sympathetic reader would care because the interdependence of structure and content makes manual skill design difficult, and a systematic method could produce skills that make agents more effective at classes of tasks. Experiments on an operations research question answering dataset indicate that the resulting optimized skills raise agent performance.

Core claim

We represent skill optimization as a bilevel problem where the outer loop uses Monte Carlo Tree Search to determine skill structure and the inner loop refines component content, with LLMs assisting in both loops, and show through evaluation on an Operations Research Question Answering dataset that the optimized skills improve the performance of the agents.

What carries the argument

Bilevel optimization framework in which Monte Carlo Tree Search explores skill structures in the outer loop and LLMs refine content in the inner loop

If this is right

The bilevel framework produces skills that raise agent performance on the evaluated operations research tasks.
Separating structure decisions from content decisions addresses the interdependence that complicates manual skill design.
LLM assistance within both loops makes search feasible in the large combined space of structures and contents.
The resulting skills can be used directly by agents to handle particular classes of tasks more effectively.

Where Pith is reading between the lines

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

The same bilevel structure might be reused to optimize agent skills for task domains other than operations research.
Iterating the optimization process over successive batches of tasks could produce skills that evolve with new data.
Measuring whether the discovered structures transfer across different base language models would test broader applicability.

Load-bearing premise

That the MCTS-driven search over structures combined with LLM content refinement discovers skills that generalize beyond the specific dataset and evaluation protocol rather than fitting the test questions.

What would settle it

Running the optimized skills on a fresh set of operations research questions drawn from the same domain but excluded from the original experiments and finding no performance gain would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.15709 by Chenyi Huang, Haoting Zhang, Jingxu Xu, Yunduan Lin, Zeyu Zheng.

**Figure 2.** Figure 2: Illustration of MCTS search tree for Configuration B in the ORQA experiment. Nodes are labeled by the [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

read the original abstract

Agent \texttt{skills} are structured collections of instructions, tools, and supporting resources that help large language model (LLM) agents perform particular classes of tasks. Empirical evidence shows that the design of \texttt{skills} can materially affect agent task performance, yet systematically optimizing \texttt{skills} remains challenging. Since a \texttt{skill} comprises instructions, tools, and supporting resources in a structured way, optimizing it requires jointly determining both the structure of these components and the content each component contains. This gives rise to a complex decision space with strong interdependence across structure and components. We therefore represent these two coupled decisions as \texttt{skill} structure and component content, and formulate \texttt{skill} optimization as a bilevel optimization problem. We propose a bilevel optimization framework in which an outer loop employs Monte Carlo Tree Search to determine the \texttt{skill} structure, while an inner loop refines the component content within the structure selected by the outer loop. In both loops, we employ LLMs to assist the optimization procedure. We evaluate the proposed framework on an open-source Operations Research Question Answering dataset, and the experimental results suggest that the bilevel optimization framework improves the performance of the agents with the optimized \texttt{skill}.

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.

Desk Editor's Note private letter to a colleague

The bilevel MCTS-LLM skill optimizer is a clean engineering formulation but the ORQA results are too thin to trust without held-out validation.

read the letter

The paper treats agent skill design as a bilevel problem where Monte Carlo Tree Search explores the high-level structure of instructions, tools, and resources while an LLM fills in the concrete content inside that structure. They run the procedure on the Operations Research Question Answering dataset and claim the resulting skills raise agent performance. That separation of structure search from content generation is the clearest new piece; most prior prompt or skill work either fixes the structure or searches everything flatly, so the explicit bilevel split is a reasonable way to handle the interdependence they describe.

Referee Report

2 major / 2 minor

Summary. The manuscript formulates skill optimization for LLM agents as a bilevel problem. The outer loop applies Monte Carlo Tree Search to explore discrete skill structures (instructions, tools, resources), while the inner loop uses LLMs to refine content within each structure. The framework is evaluated on the Operations Research Question Answering (ORQA) dataset, with the central claim that the resulting optimized skills improve agent task performance.

Significance. If the empirical gains prove robust, the bilevel MCTS-plus-LLM approach would supply a systematic, search-based method for jointly optimizing interdependent structure and content decisions in agent skills—an important practical advance for LLM agent engineering. The separation of discrete structure search from continuous content refinement is a clean modeling choice, and the use of LLMs inside the inner loop is computationally attractive. These elements would be strengthened by reproducible code or explicit falsifiable predictions, neither of which is present here.

major comments (2)

[Experimental Results] Experimental Results section: The abstract and reported results claim performance improvement on ORQA yet supply no baselines, statistical significance tests, ablation of the bilevel structure versus single-level search, or the number of structures explored by MCTS. These omissions make it impossible to determine whether the observed gains are attributable to the proposed framework.
[Methods] Methods section describing the bilevel procedure: The MCTS outer loop and LLM inner loop are executed directly on the ORQA questions used for final reporting, with no held-out validation split, cross-validation protocol, or out-of-distribution test tasks mentioned. This setup creates a direct pathway for the search to exploit dataset-specific patterns (recurring templates, answer formats) that would not generalize, directly threatening the central claim that the optimized skills reflect genuine optimization gains.

minor comments (2)

[Abstract] The abstract states that 'the experimental results suggest' improvement but does not quantify the effect size or name the precise performance metric (accuracy, F1, etc.).
[Introduction] Notation for skill components (structure versus content) is introduced without a compact diagram or table summarizing the bilevel variables, making the interdependence harder to follow on first reading.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation and strengthen the empirical support for our bilevel optimization framework. We address each major comment below and will incorporate the suggested changes in the revised manuscript.

read point-by-point responses

Referee: Experimental Results section: The abstract and reported results claim performance improvement on ORQA yet supply no baselines, statistical significance tests, ablation of the bilevel structure versus single-level search, or the number of structures explored by MCTS. These omissions make it impossible to determine whether the observed gains are attributable to the proposed framework.

Authors: We agree that the current manuscript lacks these elements, which limits interpretability of the results. In the revision, we will add: (1) baseline comparisons including standard prompting, single-level MCTS, and LLM-only refinement; (2) statistical significance testing (e.g., paired t-tests or bootstrap confidence intervals) on the reported accuracy improvements; (3) an ablation isolating the bilevel separation from single-level search; and (4) explicit reporting of MCTS parameters, including the number of structures explored and tree size. These additions will directly address whether gains stem from the proposed framework. revision: yes
Referee: Methods section describing the bilevel procedure: The MCTS outer loop and LLM inner loop are executed directly on the ORQA questions used for final reporting, with no held-out validation split, cross-validation protocol, or out-of-distribution test tasks mentioned. This setup creates a direct pathway for the search to exploit dataset-specific patterns (recurring templates, answer formats) that would not generalize, directly threatening the central claim that the optimized skills reflect genuine optimization gains.

Authors: We acknowledge this as a substantive limitation that risks overfitting to ORQA-specific artifacts. In the revised version, we will introduce a train/validation/test split of the ORQA dataset. The outer MCTS and inner LLM refinement will be performed exclusively on the training split, with validation used for structure selection and early stopping, and all final metrics reported on the held-out test set. We will also add a discussion of generalization risks and, if space permits, preliminary results on related out-of-distribution question-answering tasks to support the claim of genuine optimization. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the bilevel optimization framework or empirical claims

full rationale

The paper formulates skill optimization as a bilevel problem with an outer MCTS loop for structure and inner LLM loop for content, then reports empirical performance gains on the ORQA dataset. No equations, fitted parameters, or predictions are defined such that reported improvements reduce to the inputs by construction. There are no self-citations, uniqueness theorems, or ansatzes invoked to justify the core method; the approach is presented as a standard empirical search procedure. The derivation chain is self-contained as an algorithmic proposal plus experimental evaluation, with no load-bearing reductions to definitions or prior self-work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are identifiable from the abstract alone.

pith-pipeline@v0.9.0 · 5529 in / 1027 out tokens · 28126 ms · 2026-05-10T09:11:46.571385+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Safe Bilevel Delegation (SBD): A Formal Framework for Runtime Delegation Safety in Multi-Agent Systems
cs.AI 2026-04 unverdicted novelty 6.0

SBD is a bilevel optimization framework that learns context-dependent safety weights for runtime task delegation in hierarchical multi-agent systems, with continuous authority transfer alpha and theoretical guarantees...

Reference graph

Works this paper leans on

22 extracted references · 6 canonical work pages · cited by 1 Pith paper · 3 internal anchors

[1]

Equipping agents for the real world with agent skills, October 2025

Anthropic. Equipping agents for the real world with agent skills, October 2025

2025
[2]

SkillsBench: Benchmarking How Well Agent Skills Work Across Diverse Tasks

Xiangyi Li, Wenbo Chen, Yimin Liu, Shenghan Zheng, Xiaokun Chen, Yifeng He, Yubo Li, Bingran You, Haotian Shen, Jiankai Sun, et al. Skillsbench: Benchmarking how well agent skills work across diverse tasks.arXiv preprint arXiv:2602.12670, 2026

work page internal anchor Pith review arXiv 2026
[3]

Large language models as optimizers

Chengrun Yang, Xuezhi Wang, Yifeng Lu, Hanxiao Liu, Quoc V Le, Denny Zhou, and Xinyun Chen. Large language models as optimizers. InThe Twelfth International Conference on Learning Representations, 2023

2023
[4]

Griffiths, Yuan Cao, and Karthik Narasimhan

Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Thomas L. Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. InAdvances in Neural Information Processing Systems, volume 36, 2023

2023
[5]

Reasoning with language model is planning with world model

Shibo Hao, Yi Gu, Haodi Ma, Joshua Jiahua Hong, Zhen Wang, Daisy Zhe Wang, and Zhiting Hu. Reasoning with language model is planning with world model. InProceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, 2023

2023
[6]

Language agent tree search unifies reasoning, acting, and planning in language models

Andy Zhou, Kai Yan, Michal Shlapentokh-Rothman, Haohan Wang, and Yu-Xiong Wang. Language agent tree search unifies reasoning, acting, and planning in language models. InProceedings of the 41st International Conference on Machine Learning, volume 235 ofProceedings of Machine Learning Research, pages 62138–62160, 2024

2024
[7]

Accessing GPT-4 level Mathematical Olympiad Solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B,

Di Zhang, Xiaoshui Huang, Dongzhan Zhou, Yuqiang Li, and Wanli Ouyang. Accessing GPT-4 level mathematical olympiad solutions via Monte Carlo Tree Self-refine with LLaMa-3 8B.arXiv preprint arXiv:2406.07394, 2024

work page arXiv 2024
[8]

rStar-Math: Small LLMs can master math reasoning with self-evolved deep thinking

Xinyu Guan, Li Lyna Zhang, Yifei Liu, Ning Shang, Youran Sun, Yi Zhu, Fan Yang, and Mao Yang. rStar-Math: Small LLMs can master math reasoning with self-evolved deep thinking. InProceedings of the 42nd International Conference on Machine Learning, volume 267 ofProceedings of Machine Learning Research, pages 20640–20661. PMLR, 2025

2025
[9]

AFlow: Automating agentic workflow generation

Jiayi Zhang, Jinyu Xiang, Zhaoyang Yu, Fengwei Teng, Xionghui Chen, Jiaqi Chen, Mingchen Zhuge, Xin Cheng, Sirui Hong, Jinlin Wang, Bingnan Zheng, Bang Liu, Yuyu Luo, and Chenglin Wu. AFlow: Automating agentic workflow generation. InThe Thirteenth International Conference on Learning Representations, 2025. Oral presentation

2025
[10]

Surrogate-based simulation optimization

L Jeff Hong and Xiaowei Zhang. Surrogate-based simulation optimization. InTutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications, pages 287–311. INFORMS, 2021

2021
[11]

Fixed-confidence, fixed-tolerance guarantees for ranking-and-selection procedures.ACM Transactions on Modeling and Computer Simulation (TOMACS), 31(2):1–33, 2021

David J Eckman and Shane G Henderson. Fixed-confidence, fixed-tolerance guarantees for ranking-and-selection procedures.ACM Transactions on Modeling and Computer Simulation (TOMACS), 31(2):1–33, 2021

2021
[12]

A contextual ranking and selection method for personalized medicine.Manufacturing & Service Operations Management, 26(1):167–181, 2024

Jianzhong Du, Siyang Gao, and Chun-Hung Chen. A contextual ranking and selection method for personalized medicine.Manufacturing & Service Operations Management, 26(1):167–181, 2024

2024
[13]

Stochastic gradients: Optimization, simulation, randomization, and sensitivity analysis.IISE Transactions, 58(2):240–256, 2026

Michael C Fu, Jiaqiao Hu, and Katya Scheinberg. Stochastic gradients: Optimization, simulation, randomization, and sensitivity analysis.IISE Transactions, 58(2):240–256, 2026. 10 Bilevel Optimization of Agent Skills via Monte Carlo Tree Search

2026
[14]

V oyager: An open-ended embodied agent with large language models.Transactions on Machine Learning Research, 2024

Guanzhi Wang, Yuqi Xie, Yunfan Jiang, Ajay Mandlekar, Chaowei Xiao, Yuke Zhu, Linxi Fan, and Anima Anandkumar. V oyager: An open-ended embodied agent with large language models.Transactions on Machine Learning Research, 2024

2024
[15]

Reflexion: Language agents with verbal reinforcement learning

Noah Shinn, Federico Cassano, Ashwin Gopinath, Karthik Narasimhan, and Shunyu Yao. Reflexion: Language agents with verbal reinforcement learning. InAdvances in Neural Information Processing Systems, volume 36, 2023

2023
[16]

Reinforcement learning for self-improving agent with skill library.arXiv preprint arXiv:2512.17102, 2025

Jiongxiao Wang, Qiaojing Yan, Yawei Wang, Yijun Tian, Soumya Smruti Mishra, Zhichao Xu, Megha Gandhi, Panpan Xu, and Lin Lee Cheong. Reinforcement learning for self-improving agent with skill library.arXiv preprint arXiv:2512.17102, 2025

work page arXiv 2025
[17]

Organizing, orchestrating, and benchmarking agent skills at ecosystem scale, 2026

Hao Li, Chunjiang Mu, Jianhao Chen, Siyue Ren, Zhiyao Cui, Yiqun Zhang, Lei Bai, and Shuyue Hu. Organizing, orchestrating, and benchmarking agent skills at ecosystem scale.arXiv preprint arXiv:2603.02176, 2026

work page arXiv 2026
[18]

Agent Skills in the Wild: An Empirical Study of Security Vulnerabilities at Scale

Yi Liu, Weizhe Wang, Ruitao Feng, Yao Zhang, Guangquan Xu, Gelei Deng, Yuekang Li, and Leo Zhang. Agent skills in the wild: An empirical study of security vulnerabilities at scale.arXiv preprint arXiv:2601.10338, 2026

work page internal anchor Pith review arXiv 2026
[19]

Chain-of-thought prompting elicits reasoning in large language models.Advances in neural information processing systems, 35:24824–24837, 2022

Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models.Advances in neural information processing systems, 35:24824–24837, 2022

2022
[20]

Least-to-Most Prompting Enables Complex Reasoning in Large Language Models

Denny Zhou, Nathanael Schärli, Le Hou, Jason Wei, Nathan Scales, Xuezhi Wang, Dale Schuurmans, Claire Cui, Olivier Bousquet, Quoc Le, et al. Least-to-most prompting enables complex reasoning in large language models. arXiv preprint arXiv:2205.10625, 2022

work page internal anchor Pith review arXiv 2022
[21]

Evaluating llm reasoning in the oper- ations research domain with orqa

Mahdi Mostajabdaveh, Timothy Tin Long Yu, Samarendra Chandan Bindu Dash, Rindra Ramamonjison, Jabo Serge Byusa, Giuseppe Carenini, Zirui Zhou, and Yong Zhang. Evaluating llm reasoning in the oper- ations research domain with orqa. InProceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 24902–24910, 2025

2025
[22]

Multi-fidelity simulation optimisation for airline disruption management

Luke Rhodes-Leader, David J Worthington, Barry L Nelson, and Bhakti Stephan Onggo. Multi-fidelity simulation optimisation for airline disruption management. In2018 Winter Simulation Conference (WSC), pages 2179–2190. IEEE, 2018. 11

2018