论文标题
对马尔可夫开关随机网络的分布式优化
Distributed Optimization Over Markovian Switching Random Network
论文作者
论文摘要
在本文中，我们通过Markovian Switching通信网络研究了分布式凸优化问题。目标函数是每个代理的局部目标函数的总和，其他代理无法知道。假定通信网络可以通过马尔可夫属性切换一组重量平衡的有向图。我们提出了一个具有两个时间尺度级数的共识次级级算法，以处理马尔可夫开关拓扑并缺乏全球梯度信息的不确定性。通过适当选择步骤尺寸，我们证明，当马尔可维亚网络的联合图'的联合图紧密连接并且马尔可夫网络不可还原时，所有代理的本地局部估计几乎可以融合到相同的最佳解决方案。给出模拟以说明结果。
In this paper, we investigate the distributed convex optimization problem over a multi-agent system with Markovian switching communication networks. The objective function is the sum of each agent's local objective function, which cannot be known by other agents. The communication network is assumed to switch over a set of weight-balanced directed graphs with a Markovian property.We propose a consensus sub-gradient algorithm with two time-scale step-sizes to handle the uncertainty due to the Markovian switching topologies and the absence of global gradient information. With a proper selection of step-sizes, we prove the almost sure convergence of all agents' local estimates to the same optimal solution when the union graph of the Markovian network' states is strongly connected and the Markovian network is irreducible. Simulations are given for illustration of the results.
