HypeMARL: Multi-Agent Reinforcement Learning For High-Dimensional, Parametric, and Distributed Systems

2025-09-20

AI Summary

This work addresses the challenge of optimal control for high-dimensional, parametric, distributed systems governed by partial differential equation (PDE) constraints. We propose HypeMARL, a multi-agent reinforcement learning (MARL) framework enabling decentralized cooperative control while overcoming locality limitations. Its core innovations include: (i) a hypernetwork that jointly parameterizes policies and value functions across agents; and (ii) sinusoidal positional encoding to explicitly model agents’ relative geometric relationships, facilitating collective non-local behavior. We further extend HypeMARL to a model-based variant, MB-HypeMARL, which drastically reduces environment interaction requirements. Experiments on PDE-constrained tasks—including density regulation and flow field control—demonstrate that HypeMARL outperforms existing decentralized MARL methods in control performance, exhibits low sensitivity to hyperparameters, and achieves approximately one-order-of-magnitude reduction in interaction cost.

Technology Category

• Multiagent Systems: Adversarial Agents
• Search and Optimization: Learning to Search
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Decentralized Web and Fediverse systems

Abstract

Deep reinforcement learning has recently emerged as a promising feedback control strategy for complex dynamical systems governed by partial differential equations (PDEs). When dealing with distributed, high-dimensional problems in state and control variables, multi-agent reinforcement learning (MARL) has been proposed as a scalable approach for breaking the curse of dimensionality. In particular, through decentralized training and execution, multiple agents cooperate to steer the system towards a target configuration, relying solely on local state and reward information. However, the principle of locality may become a limiting factor whenever a collective, nonlocal behavior of the agents is crucial to maximize the reward function, as typically happens in PDE-constrained optimal control problems. In this work, we propose HypeMARL: a decentralized MARL algorithm tailored to the control of high-dimensional, parametric, and distributed systems. HypeMARL employs hypernetworks to effectively parametrize the agents' policies and value functions with respect to the system parameters and the agents' relative positions, encoded by sinusoidal positional encoding. Through the application on challenging control problems, such as density and flow control, we show that HypeMARL (i) can effectively control systems through a collective behavior of the agents, outperforming state-of-the-art decentralized MARL, (ii) can efficiently deal with parametric dependencies, (iii) requires minimal hyperparameter tuning and (iv) can reduce the amount of expensive environment interactions by a factor of ~10 thanks to its model-based extension, MB-HypeMARL, which relies on computationally efficient deep learning-based surrogate models approximating the dynamics locally, with minimal deterioration of the policy performance.

Problem

• Controls high-dimensional distributed systems using multi-agent reinforcement learning
• Addresses limitations of locality in PDE-constrained optimal control problems
• Handles parametric dependencies in complex dynamical systems efficiently

Innovation

• Uses hypernetworks to parametrize policies with system parameters
• Employs sinusoidal encoding for agents' relative positions
• Integrates model-based extension with local surrogate models