Learning Algorithms for Verification of Markov Decision Processes

We present a general framework for applying learning algorithms and heuristical guidance to the verification of Markov decision processes (MDPs), based on the ideas of Br\'azdil, T. et al. (2014). Verification of Markov Decision Processes Using Learning Algorithms. The primary goal of the techniques presented in that work is to improve performance by avoiding an exhaustive exploration of the state space, guided by heuristics. This approach is significantly extended in this work. Several details of the base theory are refined and errors are fixed. Section 1.3 provides an overview of all differences. The presented framework focuses on probabilistic reachability, which is a core problem in verification, and is instantiated in two distinct scenarios. The first assumes that full knowledge of the MDP is available, in particular precise transition probabilities. It performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP without knowing the exact transition dynamics. Here, we obtain probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. In particular, the latter is an extension of statistical model-checking (SMC) for unbounded properties in MDPs. In contrast to other related approaches, we do not restrict our attention to time-bounded (finite-horizon) or discounted properties, nor assume any particular structural properties of the MDP.