We consider a class of multi-agent optimization problems, where each agent is associated with an 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 %corresponding to 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.

中文翻译：

---

协作多智能体系统的零阶反馈优化

我们考虑一类多智能体优化问题，其中每个智能体与一个动作向量和一个局部成本相关联，目标是合作找到最小化局部成本平均值的联合动作配置文件。此类问题出现在许多应用中，例如分布式路由控制、风电场运营等。在许多这些问题中，梯度信息可能并不容易获得，并且代理可能只观察他们的行动所产生的本地成本 % 对应于他们的行动作为反馈，以确定他们的新行动。在本文中，我们为我们考虑的问题类别提出了一个零阶反馈优化方案，并为凸面和非凸面设置提供了明确的复杂性界限，并具有无噪声和有噪声的局部成本观察。我们还简要讨论了代理之间局部功能依赖性知识的影响。该算法的性能由分布式路由控制的一个数值例子证明。