# Zeroth-Order Feedback Optimization for Cooperative Multi-Agent Systems

arXiv: https://arxiv.org/abs/2011.09728 · HTML: https://mlsanity.com/paper/2011.09728/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2020.

## Built on by (most cited first, 7 of 7)

- [Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR](https://mlsanity.com/paper/2401.14534/) (2024)
- [Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies](https://mlsanity.com/paper/2210.04810/) (2022)
- [Coreset-Based Task Selection for Sample-Efficient Meta-Reinforcement Learning](https://mlsanity.com/paper/2502.02332/) (2025)
- [Asynchronous Heterogeneous Linear Quadratic Regulator Design](https://mlsanity.com/paper/2404.09061/) (2024)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Oracle Complexity Reduction for Model-free LQR: A Stochastic Variance-Reduced Policy Gradient Approach](https://mlsanity.com/paper/2309.10679/) (2023)
- [Convex and Non-convex Federated Learning with Stale Stochastic Gradients: Diminishing Step Size is All You Need](https://mlsanity.com/paper/2603.02639/) (2026)

## Abstract (arXiv)

We study a class of cooperative multi-agent optimization problems, where each agent is associated with a local action vector and a local cost, and the goal is to cooperatively find the joint action profile that minimizes the average of the local costs. Such problems arise in many applications, such as distributed routing control, wind farm operation, etc. In many of these problems, gradient information may not be readily available, and the agents may only observe their local costs incurred by their actions as a feedback to determine their new actions. In this paper, we propose a zeroth-order feedback optimization scheme for the class of problems we consider, and provide explicit complexity bounds for both the convex and nonconvex settings with noiseless and noisy local cost observations. We also discuss briefly on the impacts of knowledge of local function dependence between agents. The algorithm's performance is justified by a numerical example of distributed routing control.