| title | Bilevel Coordinated Reflection: A Game-Theoretic Approach to Multi-Agent LLM Systems |
|---|---|
| authors | Yihang Chen, Yuxiang Chen, Yuxuan Huang, Meng Fang, Weilin Luo, Jun Wang |
| date | 2026-09-02 |
| venue | arXiv (preprint, not peer reviewed) |
| id | arXiv:2609.02750 |
| upvotes | 142 (Hugging Face Daily Papers, 2026-11-01) |
| links | abs pdf hf code |
| abstract | Multi-agent LLM systems commonly use an orchestrator to decompose a task for a team of workers and then improve through textual reflection. Despite strong empirical results, these systems lack a unified account of coordination, memory improvement, and the role of external verification. We model orchestrator-worker interaction as a bilevel coordination game: under bounded coupling, the workers' local-update game is an approximate potential game whose equilibrium slack is controlled by decomposition quality. We then analyse reflection as stochastic movement over semantic memory states. For free-form reflection, we derive a finite-time upper bound, prove worst-case tightness, and give a positive lower bound under a falsifiable persistent-harm condition. We further prove an information-theoretic impossibility result: no gate that observes only the generated transcript can improve uniformly over text-indistinguishable environments, whereas an environment-grounded gate can. Motivated by this separation, we introduce Stochastic Reflective Memory Ascent (SRMA), which accepts a candidate memory only after a grounded evaluation risk strictly decreases. Under calibration and non-degenerate corrective mass, SRMA converges exactly, geometrically or polynomially; matching constructions show that both rate regimes are order-tight. We also provide confidence gating for stochastic evaluation and re-anchoring guarantees for piecewise-stationary environments. Experiments instantiate these objects with environment-grounded metrics and test the predicted coordination and drift laws. On 500 SWE-bench instances, the complete Kimi-based system resolves 72.2% versus a 70.8% public mini-SWE-agent reference. Code: https://github.com/YihangChen9/Bilevel-Coordinated-Reflection |
cite
@misc{chen2026bilevel,
title={Bilevel Coordinated Reflection: A Game-Theoretic Approach to Multi-Agent LLM Systems},
author={Yihang Chen and Yuxiang Chen and Yuxuan Huang and Meng Fang and Weilin Luo and Jun Wang},
year={2026},
eprint={2609.02750},
archivePrefix={arXiv},
url={https://arxiv.org/abs/2609.02750}
}