Uncertainty-Aware Sequential Decision Rules for Event-Triggered LLM Invocation in Streaming Systems

Streaming inference pipelines increasingly pair lightweight “fast models” with Large Language Models (LLMs) that provide rich semantic understanding at substantial cost. The central question of when to invoke the LLM has received limited formal treatment. We cast this as a risk-based sequential stopping problem, where a trigger policy π fires when a risk functional R(H_t) exceeds a threshold θ. Within this framework we prove six results: a minimum inter-event time bound excluding trigger chattering; optimality of threshold policies via smooth pasting; approximate SPRT guarantees under estimated parameters; O(√(T log T)) regret for stationary streams (extending to O(√((C_T+1) T log T)) under C_T changepoints); O(1/√T) convergence of online gradient descent for adaptive thresholds; and a calibration-to-miss-rate transfer inequality. Several classical trigger families, including event-triggered, optimal stopping, SPRT, CUSUM, and Bayesian triggers, can be expressed as special cases of this framework. On turbofan degradation data (CMAPSS) with real LLM calls, we empirically verify the theoretical assumptions, ablate the risk function design, compare against six baselines including a RouteLLM-style router and contextual bandits, and analyze cost sensitivity and LLM failure modes. The results confirm sublinear regret (α<1 for all principled triggers), high diagnostic quality (92.9% of 1,600 LLM diagnoses reach grounding score ≥0.75 under our rubric), and that anomaly-score-driven risk functions dominate alternatives by roughly an order of magnitude on the Pareto AUC.