In the distributed optimization problem for a multi-agent system, each agent knows a local function and must find a minimizer of the sum of all agents’ local functions by performing a combination of local gradient evaluations and communicating information with neighboring agents. We prove that every distributed optimization algorithm can be factored into a centralized optimization method and a second-order consensus estimator, effectively separating the “optimization” and “consensus” tasks. We illustrate this fact by providing the decomposition for many recently proposed distributed optimization algorithms. Conversely, we prove that any optimization method that converges in the centralized setting can be combined with any second-order consensus estimator to form a distributed optimization algorithm that converges in the multi-agent setting. Finally, we describe how our decomposition may lead to a more systematic algorithm design methodology.

中文翻译：

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使用增强型 f T 加倍器技术改进 InP 分频器的射频性能


在多智能体系统的分布式优化问题中，每个智能体都知道一个局部函数，并且必须通过执行局部梯度评估和与相邻智能体通信信息的组合来找到所有智能体局部函数之和的最小者。我们证明，每种分布式优化算法都可以分解为集中式优化方法和二阶共识估计器，有效分离“优化”和“共识”任务。我们通过提供许多最近提出的分布式优化算法的分解来说明这一事实。相反，我们证明任何在集中式设置中收敛的优化方法都可以与任何二阶共识估计器相结合，形成在多智能体设置中收敛的分布式优化算法。最后，我们描述了我们的分解如何导致更系统的算法设计方法。