Predictive Zonotope Reduction: Precise Runtime Monitoring under Uncertainty

Abstract

Robots operating in physical environments make control decisions based on uncertain sensor measurements, which can lead to unsafe or suboptimal actions. Runtime monitors that check their behavior against safety specifications must represent this uncertainty soundly. Zonotopes are a widely used representation, but continuously incorporating new measurements grows their order unboundedly, so monitors must periodically apply an over-approximating reduction. The choice of the reduction method substantially affects the zonotope's precision, yet existing approaches typically utilize a fixed method throughout the run, even though the optimal choice depends on the current state. This paper presents a Predictive Zonotope Reduction (PZR) approach, which frames reducer selection as an optimal control problem and solves it using beam-search model predictive control. Policy distillation into a small neural policy further provides substantially higher execution speed than model predictive control while maintaining improved performance, enabling uncertainty-aware runtime monitoring on resource-constrained real-time systems. We implement our approach in the RLola runtime monitoring framework and evaluate it on a 5-degree-of-freedom robotic arm simulated in MuJoCo, with sensor uncertainty modeled according to ISO 5725. Experiments on a Raspberry Pi 5 show that dynamic reduction significantly lowers false-positive rates in monitoring compared with static reduction strategies.