AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-21
Local Work, Global Progress: A Convergence Theory of AI Agent Collaboration
Collaboration protocols for teams of LLM agents are mostly designed empirically, so the authors 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, while a coordinator checks proposals against the global objective and merges them. They prove linear convergence up to an error floor that vanishes when the corrections are exact. With GPT-OSS-120B agents on robot routing, a three-agent team found collision-free plans in every run and outperformed a single agent controlling all robots, a six-agent team completed its search about twice as fast (median), and merging the best checked combination cut search time by about 30%.