A Canonical Form for First-Order Distributed Optimization Algorithms
A Canonical Form for First-Order Distributed Optimization Algorithms
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DOI：
10.23919/acc.2019.8814838
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
Akhil Sundararajan;Bryan Van Scoy;Laurent Lessard
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文献类型：
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作者：
Akhil Sundararajan;Bryan Van Scoy;Laurent Lessard
我们考虑的分布式优化问题，其中的代理网络的目标是最小化平均的本地功能。为了解决这个问题，最近提出了几种算法，其中代理执行与邻居的通信，局部梯度计算和更新局部状态变量的各种组合。在本文中，我们提出了一个规范形式，其特征在于任何一阶分布式算法，可以实现使用单轮的通信和梯度计算每次迭代，其中每个代理存储多达两个状态变量。规范形式具有一组最小的参数，这些参数既唯一又足够表达，可以捕获该类中的任何分布式算法。我们的规范形式的通用性，使分布式优化算法的系统分析和设计。
We consider the distributed optimization problem in which a network of agents aims to minimize the average of local functions. To solve this problem, several algorithms have recently been proposed where agents perform various combinations of communication with neighbors, local gradient computations, and updates to local state variables. In this paper, we present a canonical form that characterizes any first-order distributed algorithm that can be implemented using a single round of communication and gradient computation per iteration, and where each agent stores up to two state variables. The canonical form features a minimal set of parameters that are both unique and expressive enough to capture any distributed algorithm in this class. The generic nature of our canonical form enables the systematic analysis and design of distributed optimization algorithms.