Asynchronous and Distributed Tracking of Time-Varying Fixed Points
Asynchronous and Distributed Tracking of Time-Varying Fixed Points
复制标题
时变固定点的异步分布式跟踪
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
E. Dall’Anese
中科院分区：
文献类型：
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作者：
A. Bernstein;E. Dall’Anese
本文开发了一种用于跟踪时变收缩映射的固定点的算法框架。跟踪误差的分析结果是针对以下情况建立的：（i）底层收缩自映射在算法的每一步都发生变化； (ii) 仅有不完善的地图信息； (iii) 该算法以分布式方式实现，通信延迟和数据包丢失导致异步算法更新。分析结果适用于几类问题，包括时变凸规划基于梯度的方法的在线和异步实现中出现的时变收缩映射。在这个领域中，所提出的框架还可以捕获基于反馈的在线算法的操作原理，其中在线梯度步骤被适当修改以适应来自底层物理或逻辑网络的可操作反馈。提供了应用示例和说明性数值结果。
This paper develops an algorithmic framework for tracking fixed points of time-varying contraction mappings. Analytical results for the tracking error are established for the cases where: (i) the underlying contraction self-map changes at each step of the algorithm; (ii) only an imperfect information of the map is available; and, (iii) the algorithm is implemented in a distributed fashion, with communication delays and packet drops leading to asynchronous algorithmic updates. The analytical results are applicable to several classes of problems, including time-varying contraction mappings emerging from online and asynchronous implementations of gradient-based methods for time-varying convex programs. In this domain, the proposed framework can also capture the operating principles of feedback-based online algorithms, where the online gradient steps are suitably modified to accommodate actionable feedback from an underlying physical or logical network. Examples of applications and illustrative numerical results are provided.