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.

翻译：本文针对一般性有向多智能体网络，提出两种通信高效的分布式优化算法。第一种算法名为压缩推拉法（CPP），将梯度跟踪推拉法与通信压缩技术相结合。研究表明，CPP适用于一大类无偏压缩算子，且对强凸光滑目标函数具有线性收敛速度。第二种算法为CPP的广播式变体（B-CPP），在相同目标函数条件下同样实现线性收敛。B-CPP可应用于异步广播场景，相较于CPP进一步降低通信成本。数值实验验证了理论分析结果，证实了所提方法的有效性。