近期，实验室博士生熊永阳作为第一作者，导师吴立刚教授作为通讯作者的论文“Quantized Distributed Gradient Tracking Algorithm with Linear Convergence in Directed Networks”被国际权威期刊IEEE Transactions on Automatic Control录用。

通信效率是分布式优化算法在实际应用中遇到的主要瓶颈。为了解决该问题，量化分布式优化问题吸引了学者们的广泛关注，现有的绝大部分量化分布式优化算法收敛速度慢，只能达到次线性收敛。为了实现线性收敛，论文针对一般的有向通信网络提出了一种新颖的量化分布式梯度跟踪算法Q-DGT。论文精确给出了量化水平的下界以保证算法收敛，更重要的是，严格证明了所提算法即使在1比特通信这一极端情形下依然能够达到线性收敛，数值仿真验证了所提算法的有效性。

Abstract

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 paper 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 3 quantization levels. Numerical results also confirm the efficiency of the proposed algorithm.