Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks

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 method with communication compression. We show that CPP is applicable to class of unbiased compression operators and achieves linear convergence rate for strongly convex smooth objective functions. second algorithm broadcast-like version (B-CPP), it also under same conditions on B-CPP can be applied in an asynchronous broadcast setting further reduce costs compared CPP. Numerical experiments complement theoretical analysis confirm effectiveness proposed methods.