Hyperspace Neighbor Penetration Approach to Dynamic Programming for Model-Based Reinforcement Learning Problems with Slowly Changing Variables in A Continuous State Space

TL;DR

This paper introduces the Hyperspace Neighbor Penetration (HNP) approach for model-based reinforcement learning, enabling efficient handling of slowly changing variables in continuous state spaces by capturing partial state transitions without fine discretization.

Contribution

The paper proposes HNP, a novel method that allows coarse grid systems to effectively model slowly changing variables, improving computational efficiency over classical discretization methods.

Findings

HNP significantly outperforms classical methods in efficiency.

HNP effectively captures small state changes with coarse grids.

Successful industrial implementation demonstrates practical viability.

Abstract

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.