Quantized Distributed Gradient Tracking Algorithm With Linear Convergence in Directed Networks

Communication efficiency is a major bottleneck in the applications of distributed networks. To address the problem, the problem of quantized distributed optimization has attracted a lot of attention. However, most of the existing quantized distributed optimization algorithms can only converge sublinearly. To achieve linear convergence, this article proposes a novel quantized distributed gradient tracking algorithm (Q-DGT) to minimize a finite sum of local objective functions over directed networks. Moreover, we explicitly derive lower bounds for the number of quantization levels, and prove that Q-DGT can converge linearly even when the exchanged variables are respectively quantized with three quantization levels. Numerical results also confirm the efficiency of the proposed algorithm.

Automated summary

This article proposes a novel quantized distributed gradient tracking algorithm (Q-DGT) to address the bottleneck of communication efficiency in distributed networks. The algorithm achieves linear convergence and the numerical results confirm its efficiency.