Teams of large language model agents are increasingly used for complex tasks, but their collaboration protocols are usually designed empirically, with no formal guarantees. A new paper by Ivan Ilin and Peter Richtárik proposes a convergence theory for such collaborations, treating the process as block optimization.
In their framework, each agent improves one part of a shared solution, guided by a local objective plus a correction term that accounts for effects on other parts. A coordinator checks each proposal against the global objective and merges proposals that do not interfere. The authors prove linear convergence up to an error floor that disappears when the corrections are exact. They also show that interfering proposals can be merged after checking their combination, with the rate depending on how well the proposals actually combine rather than worst-case interactions.
The theory was tested with GPT-OSS-120B agents on robot routing. A three-agent team found collision-free plans in every run, outperforming a single agent that controlled all robots. On a larger routing task, a six-agent team completed its search about twice as fast as the single agent in median time. Merging the best checked combination of proposals, rather than only non-interfering ones, cut search time by about 30%. The convergence bound held in every round and matched observed progress. The theory was also tested on query planning in SQLite and a synthetic task.