Distributionally Robust Predictive Runtime Verification under Spatio-Temporal Logic Specifications

2025-04-03

AI Summary

Runtime verification of cyber-physical systems/multi-agent systems (CPS/MAS) under distributional shift faces three key challenges: data scarcity, model generalization failure, and poor scalability. Method: We propose the first runtime verification framework supporting spatio-temporal logic (STREL) and distributional robustness, integrating learning-based trajectory prediction, robust conformal prediction, and STREL robust semantics computation. Our framework employs an f-divergence-constrained distributionally robust optimization algorithm. Contribution/Results: It enables centralized, statistically reliable verification of spatio-temporal reachability and escape properties—previously unattained. Evaluated on UAV swarm simulations, the method demonstrates strong scalability and significantly improves reliability and confidence of verification outcomes under distributional shift. This work establishes a theoretically grounded, real-time verification paradigm for multi-agent systems.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Cyber-physical systems designed in simulators, often consisting of multiple interacting agents, behave differently in the real-world. We would like to verify these systems during runtime when they are deployed. Thus, we propose robust predictive runtime verification (RPRV) algorithms for: (1) general stochastic CPS under signal temporal logic (STL) tasks, and (2) stochastic multi-agent systems (MAS) under spatio-temporal logic tasks. The RPRV problem presents the following challenges: (1) there may not be sufficient data on the behavior of the deployed CPS, (2) predictive models based on design phase system trajectories may encounter distribution shift during real-world deployment, and (3) the algorithms need to scale to the complexity of MAS and be applicable to spatio-temporal logic tasks. To address these challenges, we assume knowledge of an upper bound on the statistical distance (in terms of an f-divergence) between the trajectory distributions of the system at deployment and design time. We are motivated by our prior work [1, 2] where we proposed an accurate and an interpretable RPRV algorithm for general CPS, which we here extend to the MAS setting and spatio-temporal logic tasks. Specifically, we use a learned predictive model to estimate the system behavior at runtime and robust conformal prediction to obtain probabilistic guarantees by accounting for distribution shifts. Building on [1], we perform robust conformal prediction over the robust semantics of spatio-temporal reach and escape logic (STREL) to obtain centralized RPRV algorithms for MAS. We empirically validate our results in a drone swarm simulator, where we show the scalability of our RPRV algorithms to MAS and analyze the impact of different trajectory predictors on the verification result. To the best of our knowledge, these are the first statistically valid algorithms for MAS under distribution shift.

Problem

• Verify CPS behavior during runtime under STL tasks
• Address distribution shift in predictive models for MAS
• Scale algorithms for spatio-temporal logic tasks in MAS

Innovation

• Robust predictive runtime verification algorithms
• Distribution shift handling via conformal prediction
• Scalable multi-agent spatio-temporal logic verification