Distributed Multi-Agent Reinforcement Learning via Distributed Model Predictive Control as a Function Approximator

Core Concepts

A novel distributed multi-agent reinforcement learning approach using distributed model predictive control as a function approximator, enabling distributed learning and deployment while avoiding nonstationarity.

Abstract

This paper presents a novel approach to multi-agent reinforcement learning (MARL) for linear systems with convex polytopic constraints. The key contributions are:

Extension of the use of model predictive control (MPC) as a function approximator in reinforcement learning to the multi-agent setting. A structured distributed MPC scheme is proposed as an approximator for the policy and value functions.

The distributed MPC scheme enables distributed learning and deployment, with only neighbor-to-neighbor communication, irrespective of the network size and topology. This avoids centralized computation and the need to share sensitive information, such as objective functions, with a central agent.

A result is provided on the relationship between the dual variables recovered distributively through the alternating direction method of multipliers (ADMM) and the optimal dual variables of the original problem. This enables the distributed learning updates to reconstruct the centralized Q-learning update, avoiding the nonstationarity issue common in MARL.

The effectiveness of the approach is demonstrated on two numerical examples: an academic example and a power systems example. The distributed learning approach is shown to outperform distributed nominal and stochastic MPC controllers, despite starting from an inaccurate model.

Stats

The paper presents the following key figures and metrics:

The error between the true optimal dual variables and those recovered from evaluating the MPC scheme with ADMM, as a function of the ADMM iteration index (Figure 1).
The evolution of the states, inputs, temporal-difference errors, and stage costs during training for the centralized and distributed approaches (Figures 2-3).
The evolution of the learnable parameters for one agent during training, comparing the centralized and distributed approaches (Figure 4).
The closed-loop cost accumulated over 100 time steps, comparing the learned policy, nominal MPC, and stochastic MPC controllers (Figure 5).
The average temporal-difference error and return per episode during training for the power systems example (Figure 6).
The evolution of the angular displacement and power flow deviation for the power systems example, comparing the first and last episodes of training (Figure 7).
The performance and number of constraint violations over 100 episodes for the power systems example, comparing the learned policy, stochastic MPC, and nominal MPC controllers (Figure 8).

Quotes

"This paper presents a novel approach to multi-agent reinforcement learning (RL) for linear systems with convex polytopic constraints."
"The use of MPC as a function approximator in RL is extended to the multi-agent setting. To this end we propose a structured convex distributed MPC scheme as an approximator for the policy and value functions, introducing a novel, model-based MARL approach for linear systems, free from nonstationary."
"We prove a result for consensus optimization; relating the dual variables recovered distributively through the alternating direction method of multipliers (ADMM) to the optimal dual variables of the original problem, that enables the distributed learning."

Key Insights Distilled From

Multi-Agent Reinforcement Learning via Distributed MPC as a Function Approximator

by Samuel Malli... at arxiv.org 04-17-2024

https://arxiv.org/pdf/2312.05166.pdf

Deeper Inquiries

How could the proposed approach be extended to handle nonlinear dynamics and non-convex constraints

To extend the proposed approach to handle nonlinear dynamics and non-convex constraints, one could consider using techniques such as nonlinear MPC (NMPC) and non-convex optimization methods.

Nonlinear MPC (NMPC): Instead of linearizing the dynamics, NMPC directly incorporates the nonlinear dynamics of the system into the optimization problem. This allows for a more accurate representation of the system behavior and can handle nonlinearities more effectively.

Non-convex Optimization: Non-convex constraints can be addressed using optimization algorithms designed for non-convex problems. Techniques such as sequential quadratic programming (SQP), interior-point methods, or genetic algorithms can be employed to handle non-convex constraints in the distributed MPC framework.

By incorporating these advanced techniques, the distributed MPC approach can be extended to handle systems with nonlinear dynamics and non-convex constraints more effectively, providing a more accurate representation of the system behavior and improving the overall performance of the learning algorithm.

What are the potential limitations or drawbacks of using distributed MPC as a function approximator compared to other approaches, such as deep neural networks

Using distributed MPC as a function approximator has several potential limitations and drawbacks compared to other approaches like deep neural networks (DNNs):

Interpretability: Distributed MPC provides a more interpretable model compared to DNNs, as the policy and value functions are based on the MPC optimization problem. However, this interpretability comes at the cost of complexity, as MPC models can be more challenging to tune and understand.

Computational Complexity: Distributed MPC involves solving optimization problems at each time step, which can be computationally intensive, especially for large-scale systems. This complexity can limit the scalability of the approach compared to simpler function approximators like DNNs.

Model Accuracy: The accuracy of the MPC-based function approximator is highly dependent on the quality of the system model. Inaccuracies in the model can lead to suboptimal performance and may require frequent updates to maintain effectiveness.

Limited Generalization: Distributed MPC may struggle with generalizing to unseen scenarios or environments, as the learning is based on the specific dynamics and constraints of the system. DNNs, on the other hand, have the potential for better generalization across a wider range of conditions.

While distributed MPC offers advantages in terms of interpretability and stability, it may face challenges in terms of computational complexity, model accuracy, and generalization compared to other function approximators like DNNs.

How could the proposed framework be adapted to handle heterogeneous agents with different dynamics, constraints, and objectives

Adapting the proposed framework to handle heterogeneous agents with different dynamics, constraints, and objectives can be achieved through the following strategies:

Agent-Specific Models: Each agent can have its own model of the system dynamics and constraints, allowing for heterogeneity in the learning process. By incorporating agent-specific models, the framework can accommodate diverse dynamics and constraints across agents.

Customized Cost Functions: Agents can have individual cost functions tailored to their specific objectives. This customization enables agents to optimize their behavior based on their unique goals while still collaborating within the multi-agent system.

Dynamic Parameter Sharing: Implementing a mechanism for dynamic parameter sharing can allow agents to exchange information about their models, constraints, and objectives. This sharing can facilitate coordination and learning among heterogeneous agents in the network.

Adaptive Learning Rates: Agents with different dynamics and constraints may require different learning rates to converge effectively. By adapting the learning rates based on the agent's characteristics, the framework can ensure efficient learning across heterogeneous agents.

By incorporating these adaptations, the proposed framework can effectively handle heterogeneous agents with varying dynamics, constraints, and objectives, enabling collaborative learning in diverse multi-agent systems.