Omega-Regular Objectives in Model-Free Reinforcement Learning

We provide the first solution for model-free reinforcement learning of \(\omega \)-regular objectives for Markov decision processes (MDPs). We present a constructive reduction from the almost-sure satisfaction of \(\omega \)-regular objectives to an almost-sure reachability problem, and extend this technique to learning how to control an unknown model so that the chance of satisfying the objective is maximized. We compile \(\omega \)-regular properties into limit-deterministic Buchi automata instead of the traditional Rabin automata; this choice sidesteps difficulties that have marred previous proposals. Our approach allows us to apply model-free, off-the-shelf reinforcement learning algorithms to compute optimal strategies from the observations of the MDP. We present an experimental evaluation of our technique on benchmark learning problems.