Title: Reinforcement Learning for Control with Probabilistic Stability Guarantee. Abstract: Reinforcement learning is promising to control dynamical systems for which the traditional control methods are hardly applicable. However, in control theory, the stability of a closed-loop system can be hardly guaranteed using the policy/controller learned solely from samples. In this paper, we will combine Lyapunov's method in control theory and stochastic analysis to analyze the mean square stability of MDP in a model-free manner. Furthermore, the finite sample bounds on the probability of stability are derived as a function of the number M and length T of the sampled trajectories. And we show that there is a lower bound on T and the probability is much more demanding for M than T. Based on the theoretical results, a REINFORCE like algorithm is proposed to learn the controller and the Lyapunov function simultaneously. 