  Recently, successful approaches have been made to exploit good-for-MDPs
automata (B\"uchi automata with a restricted form of nondeterminism) for model
free reinforcement learning, a class of automata that subsumes good for games
automata and the most widespread class of limit deterministic automata. The
foundation of using these B\"uchi automata is that the B\"uchi condition can,
for good-for-MDP automata, be translated to reachability.
  The drawback of this translation is that the rewards are, on average, reaped
very late, which requires long episodes during the learning process. We devise
a new reward shaping approach that overcomes this issue. We show that the
resulting model is equivalent to a discounted payoff objective with a biased
discount that simplifies and improves on prior work in this direction.
