用博弈论建模多智能体大模型协作，提升任务分解与反思效果。
Bilevel Coordinated Reflection: A Game-Theoretic Approach to Multi-Agent LLM Systems
- 将协调者与工作者关系建模为双层博弈，通过分解质量控制平衡点偏差。
- 证明自由反思存在有限时间上界，且在可验证条件下有正下界。
- 提出基于环境评估的反思机制，适合需高可靠性推理的系统设计。
多智能体大模型系统通常使用协调者分解任务并依靠文本反思改进。尽管实证效果良好，但缺乏对协作、记忆优化和外部验证作用的统一解释。本文将协调者-工作者互动建模为双层协调博弈：在有限耦合下，工作者的局部更新博弈近似为势博弈，其均衡松弛由任务分解质量控制。进一步分析反思为语义记忆状态间的随机转移。针对自由反思，推导出有限时间上界，证明最坏情况紧性，并在可验证的持续伤害条件下给出正下界。还证明了一个信息论不可能性结果：仅观察生成文本的门控机制无法在不可区分环境中实现一致改进，而基于环境的门控机制可以。受此启发，提出随机反射记忆上升（SRMA）算法，仅在环境基础评估风险严格下降后才接受候选记忆。在校准和非退化修正质量条件下，SRMA收敛至精确解，速率可为几何或多项式，构造证明两者阶数紧致。还提供随机评估的信心门控及分段平稳环境下的重锚定保证。实验使用环境基度量实例化上述机制，在500个SWE-bench任务上，完整基于Kimi的系统解决率达72.2%，优于70.8%的公开mini-SWE-agent参考。代码见：https://github.com/YihangChen9/Bilevel-Coordinated-Reflection
原文摘要 · Abstract (English)
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
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