论文标题
用于约束聚合优化的分布式无投影算法
Distributed Projection-free Algorithm for Constrained Aggregative Optimization
论文作者
论文摘要
在本文中，我们专注于在网络中解决分布式凸的聚合优化问题，在网络中，每个代理都有其自身的成本函数，这不仅取决于其自身的决策变量，还取决于所有代理的决策变量的汇总功能。决策变量在可行的集合中受到限制。为了最大程度地减少成本功能的总和，当每个代理只知道其本地成本功能时，我们提出了一个基于梯度跟踪的分布式Frank-Wolfe算法，其中每个节点都维护两个估计值，即代理的决策变量和全球函数梯度的估计值的估计值。该算法不含投影，但仅涉及求解线性优化以在每个步骤中获得搜索方向。我们显示了在随着时间变化的网络上提出的算法和光滑目标函数的融合。最后，我们通过数值模拟证明了所提出算法的收敛性和计算效率。
In this paper, we focus on solving a distributed convex aggregative optimization problem in a network, where each agent has its own cost function which depends not only on its own decision variables but also on the aggregated function of all agents' decision variables. The decision variable is constrained within a feasible set. In order to minimize the sum of the cost functions when each agent only knows its local cost function, we propose a distributed Frank-Wolfe algorithm based on gradient tracking for the aggregative optimization problem where each node maintains two estimates, namely an estimate of the sum of agents' decision variable and an estimate of the gradient of global function. The algorithm is projection-free, but only involves solving a linear optimization to get a search direction at each step. We show the convergence of the proposed algorithm for convex and smooth objective functions over a time-varying network. Finally, we demonstrate the convergence and computational efficiency of the proposed algorithm via numerical simulations.
