Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks

• URL: http://arxiv.org/abs/2106.07243v4
• Date: Wed, 10 Apr 2024 03:50:54 GMT
• Title: Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks
• Authors: Zhuoqing Song, Lei Shi, Shi Pu, Ming Yan,
• Abstract summary: We propose two communication efficient decentralized optimization algorithms over a general directed multi-agent network. The first algorithm combines the gradient tracking Push-Pull method with communication compression. The second algorithm is a broadcast-like version of CPP (B- CPP) and it also achieves linear convergence rate under the same conditions on the objective functions.
• Score: 17.49477125920901
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose two communication efficient decentralized optimization algorithms over a general directed multi-agent network. The first algorithm, termed Compressed Push-Pull (CPP), combines the gradient tracking Push-Pull method with communication compression. We show that CPP is applicable to a general class of unbiased compression operators and achieves linear convergence rate for strongly convex and smooth objective functions. The second algorithm is a broadcast-like version of CPP (B-CPP), and it also achieves linear convergence rate under the same conditions on 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.

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