  Shaping has proven to be a powerful but precarious means of improving
reinforcement learning performance. Ng, Harada, and Russell (1999) proposed the
potential-based shaping algorithm for adding shaping rewards in a way that
guarantees the learner will learn optimal behavior. In this note, we prove
certain similarities between this shaping algorithm and the initialization step
required for several reinforcement learning algorithms. More specifically, we
prove that a reinforcement learner with initial Q-values based on the shaping
algorithm's potential function make the same updates throughout learning as a
learner receiving potential-based shaping rewards. We further prove that under
a broad category of policies, the behavior of these two learners are
indistinguishable. The comparison provides intuition on the theoretical
properties of the shaping algorithm as well as a suggestion for a simpler
method for capturing the algorithm's benefit. In addition, the equivalence
raises previously unaddressed issues concerning the efficiency of learning with
potential-based shaping.
