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 multi-agent network using only local computation and peer-to-peer communication. In this paper, we first 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. In the second part of this paper, we propose an error feedback based compressed gradient tracking algorithm (EF-C-GT) to further improve the algorithm efficiency for biased compression operators. Numerical examples complement the theoretical findings and demonstrate the efficiency and flexibility of the proposed algorithms.

翻译：通信压缩技术对于在有限通信条件下解决分散化优化问题越来越感兴趣,全球目标是将仅使用当地计算和同行通信的多试剂网络的当地成本功能的平均值降到最低,在本文件中,我们首先提出一个新的压缩梯度跟踪算法(C-GT),将梯度跟踪技术与通信压缩相结合,特别是,C-GT与一般的压缩操作员类别相容,该类别既统一了不带偏见又不带偏见的压缩机。我们表明,C-GT继承了梯度跟踪算法的优势,并且为很强的弯曲和平稳客观功能实现了线性趋同率。在本文第二部分,我们提出了基于错误的压缩梯度跟踪算法(EF-C-GT),以进一步提高偏差压缩操作员的算法效率。数字实例补充了理论结论,并展示了拟议算法的效率和灵活性。