Local Work, Global Progress: A Convergence Theory of AI Agent Collaboration
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; t...
| Authors | Ivan Ilin, Peter Richtárik |
|---|---|
| Primary category | cs.MA |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
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