arXiv 2005.131892020-05eess.SYcs.SY

通信约束下时变有向图的分散优化

Decentralized Optimization On Time-Varying Directed Graphs Under Communication Constraints

Yiyue Chen, Abolfazl Hashemi, Haris Vikalo

摘要：

我们考虑分散优化的问题，代理的集合，每个有机会获得一个本地的代价函数，在一个随时间变化的有向网络进行通信，旨在最大限度地减少这些功能的总和。实际上，由于通信限制，代理之间可以交换的信息量是有限的。我们提出了一个通信效率的算法，分散凸优化，依赖于稀疏化的本地更新网络中相邻的代理之间交换。在有向网络中，消息稀疏化改变了列随机性--这一属性在建立分散学习任务的收敛中起着重要作用。我们提出了一个分散的优化方案，依赖于混合矩阵的局部修改，并表明它实现了$\mathcal{O}(\frac{\mathrm{ln}T}{\sqrt{T}})$收敛速度在所考虑的设置。实验结果验证了理论分析的正确性和算法的有效性。

英文摘要：

We consider the problem of decentralized optimization where a collection of agents, each having access to a local cost function, communicate over a time-varying directed network and aim to minimize the sum of those functions. In practice, the amount of information that can be exchanged between the agents is limited due to communication constraints. We propose a communication-efficient algorithm for decentralized convex optimization that rely on sparsification of local updates exchanged between neighboring agents in the network. In directed networks, message sparsification alters column-stochasticity -- a property that plays an important role in establishing convergence of decentralized learning tasks. We propose a decentralized optimization scheme that relies on local modification of mixing matrices, and show that it achieves $\mathcal{O}(\frac{\mathrm{ln}T}{\sqrt{T}})$ convergence rate in the considered settings. Experiments validate theoretical results and demonstrate efficacy of the proposed algorithm.

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摘要：

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