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

TL;DR

This paper introduces a reinforcement learning-based statistical model checking approach for verifying PCTL specifications on Markov Decision Processes, providing guarantees on error bounds and extending to both bounded and unbounded time horizons.

Contribution

It develops a novel UCB-based Q-learning method for statistical model checking of PCTL on MDPs, with provable error guarantees and extensions to unbounded specifications.

Findings

Effective verification of PCTL specifications demonstrated on case studies

Guarantees on error bounds for the proposed statistical model checking method

Extension of the approach to unbounded-time PCTL specifications

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.