Reduce, Reuse, Recycle: Categories for Compositional Reinforcement Learning

TL;DR

This paper introduces a categorical framework for compositional reinforcement learning, enabling better task decomposition, reduced complexity, and improved robustness in robotic systems learning complex behaviors.

Contribution

It applies category theory to reinforcement learning, providing a novel mathematical approach to task composition and decomposition in robotic learning.

Findings

Enables skill reduction, reuse, and recycling in robotic tasks.

Supports the categorical theory with experimental validation.

Improves system robustness and manages high-dimensional spaces.

Abstract

In reinforcement learning, conducting task composition by forming cohesive, executable sequences from multiple tasks remains challenging. However, the ability to (de)compose tasks is a linchpin in developing robotic systems capable of learning complex behaviors. Yet, compositional reinforcement learning is beset with difficulties, including the high dimensionality of the problem space, scarcity of rewards, and absence of system robustness after task composition. To surmount these challenges, we view task composition through the prism of category theory -- a mathematical discipline exploring structures and their compositional relationships. The categorical properties of Markov decision processes untangle complex tasks into manageable sub-tasks, allowing for strategical reduction of dimensionality, facilitating more tractable reward structures, and bolstering system robustness. Experimental results support the categorical theory of reinforcement learning by enabling skill reduction, reuse, and recycling when learning complex robotic arm tasks.