  Slowly changing variables in a continuous state space constitute an important
category of reinforcement learning and see its application in many domains,
such as modeling a climate control system where temperature, humidity, etc.
change slowly over time. However, this subject is less addressed in recent
studies. Classical methods with certain variants, such as Dynamic Programming
with Tile Coding which discretizes the state space, fail to handle slowly
changing variables because those methods cannot capture the tiny changes in
each transition step, as it is computationally expensive or impossible to
establish an extremely granular grid system. In this paper, we introduce a
Hyperspace Neighbor Penetration (HNP) approach that solves the problem. HNP
captures in each transition step the state's partial "penetration" into its
neighboring hyper-tiles in the gridded hyperspace, thus does not require the
transition to be inter-tile in order for the change to be captured. Therefore,
HNP allows for a very coarse grid system, which makes the computation feasible.
HNP assumes near linearity of the transition function in a local space, which
is commonly satisfied. In summary, HNP can be orders of magnitude more
efficient than classical method in handling slowly changing variables in
reinforcement learning. We have made an industrial implementation of NHP with a
great success.
