论文标题
具有积分反馈的分布式镜下降：连续时间动力学的渐近收敛分析
Distributed Mirror Descent with Integral Feedback: Asymptotic Convergence Analysis of Continuous-time Dynamics
论文作者
论文摘要
这项工作解决了分布式优化，在该优化中，代理网络希望最大程度地减少全球强烈凸目标函数。全局函数可以写为局部凸功能的总和，每个函数都与代理相关。我们提出了一种连续的时间分布式镜下降算法，该算法使用纯粹的局部信息来收敛到全局最佳。与以前在分布式镜下降上的工作不同，我们在更新中纳入了积分反馈，从而使算法在离散化时可以通过恒定的步骤收敛。我们使用Lyapunov稳定性分析建立了算法的渐近收敛性。我们进一步说明了数值实验，这些实验验证了采用积分反馈以提高分布式镜下降的收敛速率的优势。
This work 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.
