Confidence Sequences for Online Statistical Model Checking of Markov Decision Processes

Researchers present new confidence sequence methods for statistical model checking of Markov decision processes in online settings, achieving 50x sample efficiency improvements over previous approaches. The work addresses the practical problem of obtaining meaningful guarantees when exact transition probabilities are unknown, with applications to cyber-physical and biological systems.

This paper advances computational verification methodology for systems operating under uncertainty, a critical challenge in safety-critical domains. Markov decision processes serve as foundational models for decision-making in environments with both random events and controllable choices—common in autonomous systems, robotics, and biological modeling. The key innovation lies in developing confidence sequences that function efficiently in online settings, where statistical conclusions must be drawn incrementally from streaming data rather than fixed datasets.

The research context reflects a broader shift toward practical verification methods. Traditional approaches assume perfect knowledge of system parameters, an assumption rarely met in real-world deployments. Previous statistical approaches either contained subtle mathematical flaws or required prohibitively large sample sizes, creating a gap between theory and practice. This work closes that gap through mathematically rigorous confidence sequences specifically engineered for online computation.

The 50x sample efficiency improvement carries significant practical implications. In cyber-physical systems—from autonomous vehicles to medical devices—reducing sample requirements directly translates to faster deployment timelines and lower validation costs. For biological process modeling, it enables more efficient experimental design. The tool implementation makes these methods accessible beyond academic circles, democratizing access to principled uncertainty quantification.

Looking forward, this work establishes foundation for deploying formally verified autonomous systems with incomplete information. As industries increasingly adopt AI in high-stakes environments, methods that efficiently verify system behavior under uncertainty become essential infrastructure. The next phase involves integration into industrial verification workflows and evaluation on increasingly complex real-world systems.

• →New confidence sequence methods improve sample efficiency by 50x compared to previous statistical model checking approaches
• →Addresses the practical problem of verifying system behavior when exact probabilities are unknown
• →Applicable to cyber-physical systems, robotics, and biological process modeling
• →Outperforms traditional union-bound statistical approaches through optimization for online settings
• →Includes efficient tool implementation enabling practical deployment beyond theoretical research