PAC Statistical Model Checking for Markov Decision Processes and Stochastic Games
This work provides a practical solution for verifying probabilistic systems, addressing a bottleneck in fields like formal methods and AI, though it is incremental in improving efficiency over prior methods.
The authors tackled the problem of statistical model checking for Markov decision processes and stochastic games by developing an algorithm with probably approximately correct guarantees, achieving reasonably precise results within minutes for systems where previous approaches required impractically long runtimes.
Statistical model checking (SMC) is a technique for analysis of probabilistic systems that may be (partially) unknown. We present an SMC algorithm for (unbounded) reachability yielding probably approximately correct (PAC) guarantees on the results. We consider both the setting (i) with no knowledge of the transition function (with the only quantity required a bound on the minimum transition probability) and (ii) with knowledge of the topology of the underlying graph. On the one hand, it is the first algorithm for stochastic games. On the other hand, it is the first practical algorithm even for Markov decision processes. Compared to previous approaches where PAC guarantees require running times longer than the age of universe even for systems with a handful of states, our algorithm often yields reasonably precise results within minutes, not requiring the knowledge of mixing time or the topology of the whole model.