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This paper formalizes slow-module invocation in dual-system VLA models as a decision-theoretic problem, introducing the Value of Intervention (VoI) as a unifying quantity for scheduling mechanisms. It establishes a renewal baseline as optimal under state-independent collapse and derives adaptive gains dependent on cost ratio and collapse dispersion. Empirical validation across diverse systems and tasks demonstrates that adaptive scheduling aligns with theoretical predictions, while highlighting limitations in current language-rewrite channels and proposing a leak-free protocol for improved early-warning detection.
Adaptive scheduling for slow VLA modules can be optimized by a single, measurable quantity, the Value of Intervention, revealing that language-rewrite channels often fail to translate invoked queries into success.
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 $\rho$ and the dispersion of collapse. Measured systems span three orders of magnitude in $\rho$ (FiS-VLA $0.95$; RoboICL about $10^3$), and a direct test confirms the low-$\rho$ prediction: calibrated gains vanish under homogeneous collapse and grow with heterogeneity. Fourteen closed-loop arms on LIBERO test the contested middle of the continuum ($\rho=1.53$): 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.