Reinforcement Learning with Function-Valued Action Spaces for Partial Differential Equation Control

TL;DR

This paper introduces a novel reinforcement learning approach for controlling PDEs with high-dimensional, spatially-regular action spaces by using action descriptors, improving sample efficiency and control performance.

Contribution

It proposes the concept of action descriptors for PDE control, enabling RL to handle high-dimensional, spatially-structured actions more effectively.

Findings

Action descriptors improve sample efficiency in PDE control tasks.

The approach outperforms conventional methods in high-dimensional settings.

Experiments demonstrate effectiveness on PDE control problems with up to 256 actions.

Abstract

Recent work has shown that reinforcement learning (RL) is a promising approach to control dynamical systems described by partial differential equations (PDE). This paper shows how to use RL to tackle more general PDE control problems that have continuous high-dimensional action spaces with spatial relationship among action dimensions. In particular, we propose the concept of action descriptors, which encode regularities among spatially-extended action dimensions and enable the agent to control high-dimensional action PDEs. We provide theoretical evidence suggesting that this approach can be more sample efficient compared to a conventional approach that treats each action dimension separately and does not explicitly exploit the spatial regularity of the action space. The action descriptor approach is then used within the deep deterministic policy gradient algorithm. Experiments on two PDE control problems, with up to 256-dimensional continuous actions, show the advantage of the proposed approach over the conventional one.