First convergence theory for LLM agent teams proves linear rate, 2x speedup on routing
peter_richtarik · x · 2026-10-22
arXiv paper "Local Work, Global Progress" (Ilin & Richtárik) formalizes LLM agent collaboration as block optimization: each agent improves one block of a shared solution with a correction for cross-block interference, while a coordinator verifies proposals against the global objective and merges non-interfering (or verified-composable) ones. They prove linear convergence to an error floor that vanishes with exact corrections. With GPT-OSS-120B agents on robot routing, a three-agent team found collision-free plans in all 40 runs, beating a single agent; six agents completed search 2x faster (median), and merging best verified combinations cut search time 30%. Measured constants (μ=0.43–0.70, κ≈1.2–1.5) make the bound track observed progress within 3–7x in every round. Also covers learned corrections, private steps vs. synchronization, SQLite query planning, and a synthetic task with certified constants. 59 pages.
Related event: First Convergence Theory for AI Agent Collaboration via Block Optimization(6 posts)→
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