  Although in recent years reinforcement learning has become very popular the
number of successful applications to different kinds of operations research
problems is rather scarce. Reinforcement learning is based on the well-studied
dynamic programming technique and thus also aims at finding the best stationary
policy for a given Markov Decision Process, but in contrast does not require
any model knowledge. The policy is assessed solely on consecutive states (or
state-action pairs), which are observed while an agent explores the solution
space. The contributions of this paper are manifold. First we provide deep
theoretical insights to the widely applied standard discounted reinforcement
learning framework, which give rise to the understanding of why these
algorithms are inappropriate when permanently provided with non-zero rewards,
such as costs or profit. Second, we establish a novel near-Blackwell-optimal
reinforcement learning algorithm. In contrary to former method it assesses the
average reward per step separately and thus prevents the incautious combination
of different types of state values. Thereby, the Laurent Series expansion of
the discounted state values forms the foundation for this development and also
provides the connection between the two approaches. Finally, we prove the
viability of our algorithm on a challenging problem set, which includes a
well-studied M/M/1 admission control queuing system. In contrast to standard
discounted reinforcement learning our algorithm infers the optimal policy on
all tested problems. The insights are that in the operations research domain
machine learning techniques have to be adapted and advanced to successfully
apply these methods in our settings.
