Model-Free Reinforcement Learning for Stochastic Games with Linear Temporal Logic Objectives

We study synthesis of control strategies from linear temporal logic (LTL) objectives in unknown environments. We model this problem as a turn-based zero-sum stochastic game between the controller and the environment, where the transition probabilities and the model topology are fully unknown. The winning condition for the controller in this game is the satisfaction of the given LTL specification, which can be captured by the acceptance condition of a deterministic Rabin automaton (DRA) directly derived from the LTL specification. We introduce a model-free reinforcement learning (RL) methodology to find a strategy that maximizes the probability of satisfying a given LTL specification when the Rabin condition of the derived DRA has a single accepting pair. We then generalize this approach to any LTL formulas, for which the Rabin accepting condition may have more than one pairs, providing a lower bound on the satisfaction probability. Finally, we show applicability of our RL method on two planning case studies.