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. We consider the setting where gradient information is not readily available, and the agents only observe their local costs incurred by their actions as a feedback to determine their new actions. We propose a zeroth-order feedback optimization scheme and provide explicit complexity bounds for the constrained convex setting 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.

我们研究了一类协作多智能体优化问题，其中每个智能体都与一个局部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。我们考虑梯度信息不容易获得的设置，并且智能体仅观察他们的行为所产生的本地成本作为反馈来确定他们的新行为。我们提出了一种零阶反馈优化方案，并为具有无噪声和噪声局部成本观测值的受限凸设置提供了明确的复杂性界限。我们还简要讨论了代理之间局部函数依赖知识的影响。该算法的性能由分布式路由控制的数值示例证明。