New paper proves linear convergence for LLM agent teams via block optimization
peter_richtarik · x · 2026-10-22
Peter Richtárik and Ivan Ilin posted the arXiv paper "Local Work, Global Progress: A Convergence Theory of AI Agent Collaboration", giving LLM multi-agent collaboration its first convergence guarantees.
- Modeling: collaborative problem solving as block optimization—each agent improves one block of a shared solution using a local objective plus a correction for cross-effects; a coordinator checks proposals against the global objective and merges non-interfering ones
- Theory: linear convergence up to an error floor that vanishes when corrections are exact; checked interfering proposals can also be merged, with rates depending on how well proposals combine rather than worst-case interactions
- Experiments (GPT-OSS-120B): on robot routing, a three-agent team found collision-free plans in every run, beating a single agent; a six-agent team completed a larger search 2x faster (median); merging the best checked combination cut search time 30%
- Also validated on SQLite query planning and a synthetic task; convergence bounds with measured constants tracked observed progress every round
Related event: First Convergence Theory for AI Agent Collaboration via Block Optimization(6 posts)→
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