Verification of Markov Decision Processes using Learning Algorithms?

Abstract. We present a general framework for applying machine-learning algo-rithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive ex-ploration of the state space. Our framework focuses on probabilistic reachability, which is a core property for verification, and is illustrated through two distinct instantiations. The first assumes that full knowledge of the MDP is available, and performs a heuristic-driven partial exploration of the model, yielding pre-cise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP, and yields probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stop-ping criteria for the approximation. The latter is the first extension of statistical model checking for unbounded properties in MDPs. In contrast with other related techniques, our approach is not restricted to time-bounded (finite-horizon) or dis-counted properties, nor does it assume any particular properties of the MDP. We also show how our methods extend to LTL objectives. We present experimental results showing the performance of our framework on several examples.