论文标题
通过线性收敛进行分散优化的压缩梯度跟踪方法
A Compressed Gradient Tracking Method for Decentralized Optimization with Linear Convergence
论文作者
论文摘要
通信压缩技术是在有限的通信下解决分散优化问题的日益兴趣，在这种情况下，全球目标是仅使用本地计算和点对点通信来最大程度地减少多机构网络上本地成本函数的平均功能。在本文中，我们提出了一种新型的压缩梯度跟踪算法（C-GT），将梯度跟踪技术与通信压缩结合在一起。特别是，C-GT与统一无偏和偏置压缩机的一般压缩操作员兼容。我们表明，C-GT继承了基于梯度跟踪算法的优势，并实现了强烈凸和光滑目标函数的线性收敛速率。数值示例补充了理论发现，并证明了所提出的算法的效率和灵活性。
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 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.
