Bilevel Coordinated Reflection: A Game-Theoretic Approach to Multi-Agent LLM Systems
Paper models multi-agent LLM orchestration as a bilevel game, proving transcript-only gating limits and introducing grounded-memory SRMA.
A new paper frames orchestrator-worker coordination in multi-agent LLM systems as a bilevel coordination game and analyzes free-form reflection as stochastic movement over semantic memory states, deriving finite-time bounds and an information-theoretic impossibility result: no gate observing only the generated transcript can uniformly improve over text-indistinguishable environments, while an environment-grounded gate can. The authors propose Stochastic Reflective Memory Ascent (SRMA), which accepts candidate memory only when grounded evaluation risk strictly decreases, with geometric or polynomial convergence guarantees. On 500 SWE-bench instances, a Kimi-based instantiation of the full system resolves 72.2% versus a 70.8% public mini-SWE-agent reference.
- Proves no transcript-only gate can uniformly improve over text-indistinguishable environments; environment-grounded gates can.
- Introduces SRMA, accepting memory updates only when grounded evaluation risk strictly decreases.
- Kimi-based system resolves 72.2% of 500 SWE-bench instances versus a 70.8% mini-SWE-agent reference.
Full article223 words · extracted from huggingface.co · click to collapse
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
Text extracted automatically; images, tables and formatting may be missing. Original: https://huggingface.co/papers/2609.02750