Optimization theory says agent teams get a cost-optimal sync interval, not a safe maximum

peter_richtarik · x · 2026-11-02

Peter Richtarik explains his team's paper "Local Work, Global Progress: A Convergence Theory of AI Agent Collaboration," answering how rarely AI agent teams can sync before progress stalls:

The theory yields a cost-optimal sync interval, not a maximum safe interval beyond which progress suddenly stalls.
Each round, agents take H private steps against the same frozen shared solution; guaranteed per-round contraction is α(H) = μ·q(H)/κ with q(H) = 1−(1−ρ)^H, and per-unit-time progress is α(H)/(cH+C). Costlier syncing favors longer local work — per-round progress can rise while progress per unit time falls.
With exact corrections, any fixed H ≥ 1 converges with repeated syncs; skipping syncs forever fails since a frozen subproblem misses other agents' gains.
With inexact corrections, local work can't compensate for missing information; drift-with-staleness is not modeled — a useful future extension.

Directly relevant to multi-agent engineering trade-offs between local steps and coordination cost.

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Optimization theory says agent teams get a cost-optimal sync interval, not a safe maximum

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