Reinforcement Learning for Infinite-Dimensional Systems

TL;DR

This paper introduces a novel reinforcement learning framework for large-scale, infinite-dimensional systems, utilizing a kernel transform and hierarchical algorithms to efficiently learn optimal policies in complex, high-dimensional environments.

Contribution

It proposes a new RL architecture with a moment kernel transform and hierarchical algorithms tailored for infinite-dimensional systems, addressing computational challenges.

Findings

The algorithm converges rapidly due to early stopping and spectral sequence construction.

Validated on engineering and quantum system examples, demonstrating efficiency and effectiveness.

Provides a scalable RL approach for large, complex systems modeled in infinite-dimensional spaces.

Abstract

Interest in reinforcement learning (RL) for large-scale systems, comprising extensive populations of intelligent agents interacting with heterogeneous environments, has surged significantly across diverse scientific domains in recent years. However, the large-scale nature of these systems often leads to high computational costs or reduced performance for most state-of-the-art RL techniques. To address these challenges, we propose a novel RL architecture and derive effective algorithms to learn optimal policies for arbitrarily large systems of agents. In our formulation, we model such systems as parameterized control systems defined on an infinite-dimensional function space. We then develop a moment kernel transform that maps the parameterized system and the value function into a reproducing kernel Hilbert space. This transformation generates a sequence of finite-dimensional moment representations for the RL problem, organized into a filtrated structure. Leveraging this RL filtration, we develop a hierarchical algorithm for learning optimal policies for the infinite-dimensional parameterized system. To enhance the algorithm's efficiency, we exploit early stopping at each hierarchy, demonstrating the fast convergence property of the algorithm through the construction of a convergent spectral sequence. The performance and efficiency of the proposed algorithm are validated using practical examples in engineering and quantum systems.