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

Abstract

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. Measured systems span three orders of magnitude in $ρ$ (FiS-VLA $0.95$; RoboICL about $10^3$), and a direct test confirms the low-$ρ$ prediction: calibrated gains vanish under homogeneous collapse and grow with heterogeneity. Fourteen closed-loop arms on LIBERO test the contested middle of the continuum ($ρ=1.53$): the adaptive trigger allocates its queries exactly as the threshold rule predicts, yet the language-rewrite channel cannot convert them into success on either suite, and a revert actuator that undoes a failed rewrite is the only intervention with zero net downside on both LIBERO-Spatial and LIBERO-Goal, where the rewrite deficit deepens from thirteen to forty-two points. A four-measure leak-free protocol cuts apparent early-warning AUC from $0.93$ to $0.62$ on $929$ deployment traces, a detection-limited frontier theorem converts detection quality into a schedulability statement, and a compilation loop turns measured value functions into per-task refresh periods within $2.4\%$ of the closed-loop oracle. Together these results turn slow-module invocation from a design opinion into a measured decision.