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Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks
arXiv - CS - Distributed, Parallel, and Cluster Computing Pub Date : 2021-06-14 , DOI: arxiv-2106.07243 Zhuoqing Song, Lei Shi, Shi Pu, Ming Yan
arXiv - CS - Distributed, Parallel, and Cluster Computing Pub Date : 2021-06-14 , DOI: arxiv-2106.07243 Zhuoqing Song, Lei Shi, Shi Pu, Ming Yan
In this paper, we propose two communication-efficient algorithms for
decentralized optimization over a multi-agent network with general directed
network topology. In the first part, we consider a novel
communication-efficient gradient tracking based method, termed Compressed
Push-Pull (CPP), which combines the Push-Pull method with communication
compression. We show that CPP is applicable to a general class of unbiased
compression operators and achieves linear convergence for strongly convex and
smooth objective functions. In the second part, we propose a broadcast-like
version of CPP (B-CPP), which also achieves linear convergence rate under the
same conditions for the objective functions. B-CPP can be applied in an
asynchronous broadcast setting and further reduce communication costs compared
to CPP. Numerical experiments complement the theoretical analysis and confirm
the effectiveness of the proposed methods.
中文翻译:
通用有向网络上分散优化的压缩梯度跟踪
在本文中,我们提出了两种通信高效算法,用于在具有通用有向网络拓扑的多代理网络上进行分散优化。在第一部分中,我们考虑了一种新的基于通信高效梯度跟踪的方法,称为压缩推挽(CPP),它将推挽方法与通信压缩相结合。我们表明 CPP 适用于一般类别的无偏压缩算子,并实现强凸和平滑目标函数的线性收敛。在第二部分中,我们提出了一种类似广播的 CPP(B-CPP)版本,它在目标函数的相同条件下也实现了线性收敛速度。B-CPP 可以应用于异步广播设置,与 CPP 相比进一步降低通信成本。
更新日期:2021-06-15
中文翻译:
通用有向网络上分散优化的压缩梯度跟踪
在本文中,我们提出了两种通信高效算法,用于在具有通用有向网络拓扑的多代理网络上进行分散优化。在第一部分中,我们考虑了一种新的基于通信高效梯度跟踪的方法,称为压缩推挽(CPP),它将推挽方法与通信压缩相结合。我们表明 CPP 适用于一般类别的无偏压缩算子,并实现强凸和平滑目标函数的线性收敛。在第二部分中,我们提出了一种类似广播的 CPP(B-CPP)版本,它在目标函数的相同条件下也实现了线性收敛速度。B-CPP 可以应用于异步广播设置,与 CPP 相比进一步降低通信成本。