Newest papers

Local Work, Global Progress: A Convergence Theory of AI Agent Collaboration

Ivan Ilin, Peter Richtárik · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.28286 · cited by 0 works (OpenAlex) · open-access PDF

Portuguese

As equipes de agentes de grande modelo de linguagem (LLM) são cada vez mais aplicadas a tarefas complexas, mas seus protocolos de colaboração são principalmente projetados empiricamente, sem garantias de convergência. Formalizamos a solução de problemas colaborativa como otimização de blocos: cada agente melhora uma parte de uma solução compartilhada, guiada por seu objetivo local mais uma correção de como suas mudanças afetam as outras partes. Um coordenador verifica cada proposta contra o objetivo global e fusiona propostas que não interferem umas com as outras. Provámo convergência de linha até um piso de erro que desaparece quando as correções são exatas. As propostas de interferência também podem ser fundidas uma vez que sua combinação foi verificada; a taxa depende de quão bem as propostas realmente se combinam, não nas interações

Machine translation (Meta M2M100); the English original follows.

Abstract

Teams of large language model (LLM) agents are increasingly applied to complex tasks, but their collaboration protocols are mostly designed empirically, without convergence guarantees. We formalize collaborative problem solving as block optimization: each agent improves one part of a shared solution, guided by its local objective plus a correction for how its changes affect the other parts. A coordinator checks every proposal against the global objective and merges proposals that do not interfere with each other. We prove linear convergence up to an error floor that vanishes when the corrections are exact. Interfering proposals can also be merged once their combination has been checked; the rate then depends on how well the proposals actually combine, not on worst-case interactions. With GPT-OSS-120B agents on robot routing, a three-agent team finds collision-free plans in every run, better than those of a single agent that controls all robots. On a larger routing task, a six-agent team completes its search about twice as fast as the single agent (in median). Merging the best checked combination of proposals, rather than only proposals that do not interfere, cuts the team's search time by about 30%. With constants measured on the runs, our convergence bound holds in every round and follows the observed progress. We also test the theory on query planning in SQLite and on a synthetic task.

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Topics: Convergence (economics), Computer science, Mathematical optimization, Block (permutation group theory), Constant (computer programming), Routing (electronic design automation)

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