Ivan Ilin, Peter Richtárik · 2026 · arXiv
DOI: 10.48550/arXiv.2610.28286 · open-access PDF
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 correctio
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