  We study the problem of synthesizing control strategies for 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 LTL formulas for
which the Rabin condition has a larger number of accepting pairs, providing a
lower bound on the satisfaction probability. Finally, we illustrate
applicability of our RL method on two motion planning case studies.
