When to Ask for Help: A Decision-Theoretic Account and Measurement Standard for Slow-Module Scheduling in Dual-System Vision-Language-Action Models

Dual-system vision-language-action (VLA) models pair a high-frequency fast policy with a slow, expensive module, and published trigger mechanisms for invoking it lack a shared objective, measured costs, and any standard separating schedule quality from module quality. We provide the missing account: invocation is formalized as a calibrated decision problem whose fixed-ratio, fixed-budget, and history-gated schedules are degenerate cases of one quantity, the Value of Intervention (VoI); a renewal baseline proves the optimal schedule periodic under state-independent collapse, with adaptive gains governed by the cost ratio ρ and the dispersion of collapse.

From the abstract. Our summary is in progress.