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.
翻译:我们研究一组合作性多试剂优化问题,每个代理商都与当地行动矢量和当地成本相关联,目标是合作寻找联合行动概况,最大限度地减少当地成本的平均值,这些问题在许多应用中出现,例如分布式航线控制、风力农场运作等。在很多这些问题中,梯度信息可能不容易获得,代理商只能观察其行动造成的当地成本,作为确定新行动的反馈。在本文件中,我们为我们所考虑的问题类别提出了一个零级反馈优化计划,并为螺旋形和非螺旋形设置提供明确的复杂界限,同时进行无噪音和噪音的本地成本观察。我们还简要讨论了对代理人之间对当地功能依赖性知识的影响。算法的绩效依据是分布式路由控制的数字示例。