Statistically Model Checking PCTL Specifications on Markov Decision Processes via Reinforcement Learning

Abstract

Probabilistic Computation Tree Logic (PCTL) is frequently used to formally specify control objectives such as probabilistic reachability and safety. In this work, we focus on model checking PCTL specifications statistically on Markov Decision Processes (MDPs) by sampling, e.g., checking whether there exists a feasible policy such that the probability of reaching certain goal states is greater than a threshold. We use reinforcement learning to search for such a feasible policy for PCTL specifications, and then develop a statistical model checking (SMC) method with provable guarantees on its error. Specifically, we first use upper-confidence-bound (UCB) based Q-learning to design an SMC algorithm for bounded-time PCTL specifications, and then extend this algorithm to unbounded-time specifications by identifying a proper truncation time by checking the PCTL specification and its negation at the same time. Finally, we evaluate the proposed method on case studies.

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• Algorithms for multi-armed bandit problems
• Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints
• Environment-Independent Task Specifications via GLTL
• PAC Statistical Model Checking for Markov Decision Processes and Stochastic Games
• Reinforcement Learning With Temporal Logic Rewards