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. A key feature of our technique is the compilation of {\omega}-regular properties into limit- deterministic Buechi 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.
@article{arxiv.1810.00950,
title = {Omega-Regular Objectives in Model-Free Reinforcement Learning},
author = {Ernst Moritz Hahn and Mateo Perez and Sven Schewe and Fabio Somenzi and Ashutosh Trivedi and Dominik Wojtczak},
journal= {arXiv preprint arXiv:1810.00950},
year = {2018}
}