Communication compression techniques are of growing interests in studying the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over networked agents 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.  We show that C-GT inherits the advantages of gradient tracking-based algorithms , and in particular, achieves linear convergence rate for strongly convex and smooth objective functions. Numerical examples further demonstrate the efficiency and flexibility of the proposed algorithm .
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 .
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in studying
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networked agents
a multi-agent network
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In particular, C-GT is compatible with a general class of compression operators that unifies both unbiased and biased compressors.
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, and in particular,
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Numerical examples further
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
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