Sound Statistical Model Checking for Probabilities and Expected Rewards

2024-11-01

International Conference on Tools and Algorithms for Construction and Analysis of Systems

AI Summary

Statistical Model Checking (SMC) often yields inflated error rates in probabilistic and expected reward estimation due to insufficient statistical rigor. To address this, we propose a robust estimation framework with rigorous theoretical guarantees: (i) we extend the Dvoretzky–Kiefer–Wolfowitz (DKW) inequality to expected reward estimation for the first time; (ii) we introduce a limit-PAC (Probably Approximately Correct) procedure ensuring controllable estimation error; and (iii) we derive a computable upper bound on reachability rewards and enhance practicality via path truncation and distribution bounding. Our method is implemented in the *modes* tool. Experimental evaluation demonstrates a substantial reduction in erroneous conclusions while maintaining high precision, thereby ensuring both statistical correctness and engineering applicability.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Statistical model checking estimates probabilities and expectations of interest in probabilistic system models by using random simulations. Its results come with statistical guarantees. However, many tools use unsound statistical methods that produce incorrect results more often than they claim. In this paper, we provide a comprehensive overview of tools and their correctness, as well as of sound methods available for estimating probabilities from the literature. For expected rewards, we investigate how to bound the path reward distribution to apply sound statistical methods for bounded distributions, of which we recommend the Dvoretzky-Kiefer-Wolfowitz inequality that has not been used in SMC so far. We prove that even reachability rewards can be bounded in theory, and formalise the concept of limit-PAC procedures for a practical solution. The 'modes' SMC tool implements our methods and recommendations, which we use to experimentally confirm our results.

Problem

• Evaluating correctness of statistical model checking tools
• Developing sound methods for probability estimation
• Establishing bounds for expected reward distributions

Innovation

• Sound statistical methods for probability estimation
• Dvoretzky-Kiefer-Wolfowitz inequality for bounded rewards
• Limit-PAC procedures for practical reachability analysis