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.