分布式Optimization的扩散自适应策略及网络学习
Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks
摘要：
我们提出了一种自适应扩散机制，以优化全局费用函数在一个网络的节点分布的方式。假设费用函数由各个分量的集合组成。扩散自适应允许节点实时合作和扩散信息;它还有助于通过连续学习过程减轻随机梯度噪声和测量噪声的影响。我们分析了算法的均方误差性能的一些细节，包括其瞬态和稳态行为。我们还将扩散算法应用于两个问题：稀疏参数的分布式估计和分布式定位。与研究充分的增量方法相比，扩散方法不需要在节点上使用循环路径，并且对节点和链路故障具有鲁棒性。扩散方法还赋予网络自适应能力，即使当费用函数随时间变化时，也使各个节点能够继续学习。涉及具有移动目标的这种动态费用函数的示例在生物网络的上下文中是常见的。
英文摘要：
We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the nodes to cooperate and diffuse information in real-time; it also helps alleviate the effects of stochastic gradient noise and measurement noise through a continuous learning process. We analyze the mean-square-error performance of the algorithm in some detail, including its transient and steady-state behavior. We also apply the diffusion algorithm to two problems: distributed estimation with sparse parameters and distributed localization. Compared to well-studied incremental methods, diffusion methods do not require the use of a cyclic path over the nodes and are robust to node and link failure. Diffusion methods also endow networks with adaptation abilities that enable the individual nodes to continue learning even when the cost function changes with time. Examples involving such dynamic cost functions with moving targets are common in the context of biological networks.
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