Communication compression techniques are of growing interests for solving the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over a multiagent network using only local computation and peer-to-peer communication. In this article, we propose a novel compressed gradient tracking algorithm (C-GT) that combines gradient tracking technique with communication compression. In particular, C-GT is compatible with a general class of compression operators that unifies both unbiased and biased compressors. We show that C-GT inherits the advantages of gradient tracking-based algorithms and achieves linear convergence rate for strongly convex and smooth objective functions. Numerical examples complement the theoretical findings and demonstrate the efficiency and flexibility of the proposed algorithm.

中文翻译：

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线性收敛的分散优化的压缩梯度跟踪方法


通信压缩技术对于解决有限通信下的分散优化问题越来越感兴趣，其中全局目标是仅使用本地计算和对等通信来最小化多代理网络上本地成本函数的平均值。在本文中，我们提出了一种新颖的压缩梯度跟踪算法（C-GT），它将梯度跟踪技术与通信压缩相结合。特别是，C-GT 与统一无偏压缩器和有偏压缩器的通用压缩运算符兼容。我们证明了 C-GT 继承了基于梯度跟踪的算法的优点，并且对于强凸且平滑的目标函数实现了线性收敛速度。数值例子补充了理论结果，并证明了所提出算法的效率和灵活性。