Reduce, Reuse, Recycle: Categories for Compositional Reinforcement Learning

2024-08-23

European Conference on Artificial Intelligence

AI Summary

Multi-task reinforcement learning (RL) faces challenges including high-dimensional state spaces, sparse rewards, and poor policy robustness. To address these, this work introduces category theory as a foundational framework for RL—marking the first systematic application of categorical principles to model the structure and composability of Markov decision processes (MDPs) axiomatically, revealing their functorial nature and natural transformation mechanisms. We propose a functional RL framework grounded in universal properties, enabling provably sound skill abstraction, structure-preserving policy transfer, and composable task decomposition, reuse, and reconstruction. Evaluated on complex robotic manipulation tasks, our approach significantly improves cross-task generalization and sample efficiency, mitigates the curse of dimensionality, and enhances policy robustness. This work establishes a novel theoretical foundation and practical methodology for verifiable, composable agent learning.

Technology Category

• Machine Learning: Reinforcement Learning
• Multiagent Systems: Multiagent Learning
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Task composition in reinforcement learning is challenging due to high dimensionality.
• Scarcity of rewards and lack of robustness hinder task decomposition.
• Category theory helps reduce dimensionality and improve system robustness.

Innovation

• Uses category theory for task decomposition.
• Reduces dimensionality via categorical properties.
• Enhances system robustness and reward structures.