  One major limitation to the applicability of Reinforcement Learning (RL) to
many practical domains is the large number of samples required to learn an
optimal policy. To address this problem and improve learning efficiency, we
consider a linear hierarchy of abstraction layers of the Markov Decision
Process (MDP) underlying the target domain. Each layer is an MDP representing a
coarser model of the one immediately below in the hierarchy. In this work, we
propose a novel form of Reward Shaping where the solution obtained at the
abstract level is used to offer rewards to the more concrete MDP, in such a way
that the abstract solution guides the learning in the more complex domain. In
contrast with other works in Hierarchical RL, our technique has few
requirements in the design of the abstract models and it is also tolerant to
modeling errors, thus making the proposed approach practical. We formally
analyze the relationship between the abstract models and the exploration
heuristic induced in the lower-level domain. Moreover, we prove that the method
guarantees optimal convergence and we demonstrate its effectiveness
experimentally.
