Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks
This work addresses communication bottlenecks in decentralized multi-agent systems, offering incremental improvements for applications like distributed machine learning.
The paper tackles decentralized optimization over directed networks by proposing two communication-efficient algorithms, Compressed Push-Pull (CPP) and its broadcast version (B-CPP), which achieve linear convergence rates for strongly convex and smooth functions, with B-CPP further reducing communication costs in asynchronous settings.
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.