Distributed Mirror Descent With Integral Feedback: Asymptotic Convergence Analysis of Continuous-Time Dynamics
Distributed Mirror Descent With Integral Feedback: Asymptotic Convergence Analysis of Continuous-Time Dynamics
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DOI：
10.1109/lcsys.2020.3040934
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发表时间：
2020-11
影响因子：
3
通讯作者：
Youbang Sun;Shahin Shahrampour
中科院分区：
文献类型：
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作者：
Youbang Sun;Shahin Shahrampour
这封信解决分布式优化，其中代理网络希望最小化全局强凸目标函数。全局函数可以写成局部凸函数的和，每个局部凸函数与一个代理相关联。我们提出了一个连续时间分布式镜像下降算法，使用纯粹的本地信息收敛到全局最优。与以前的分布式镜像下降的工作不同，我们在更新中加入了积分反馈，使算法在离散化时以恒定的步长收敛。利用李雅普诺夫稳定性分析证明了该算法的渐进收敛性。我们进一步说明了数值实验，验证了采用积分反馈的优点，以提高分布式镜像下降的收敛速度。
This letter addresses distributed optimization, where a network of agents wants to minimize a global strongly convex objective function. The global function can be written as a sum of local convex functions, each of which is associated with an agent. We propose a continuous-time distributed mirror descent algorithm that uses purely local information to converge to the global optimum. Unlike previous work on distributed mirror descent, we incorporate an integral feedback in the update, allowing the algorithm to converge with a constant step-size when discretized. We establish the asymptotic convergence of the algorithm using Lyapunov stability analysis. We further illustrate numerical experiments that verify the advantage of adopting integral feedback for improving the convergence rate of distributed mirror descent.