Liu Jie, Yu Zhan, Ho Daniel W C
IEEE Trans Neural Netw Learn Syst. 2022 May 12;PP. doi: 10.1109/TNNLS.2022.3172450.
In this article, we consider a distributed constrained optimization problem with delayed subgradient information over the time-varying communication network, where each agent can only communicate with its neighbors and the communication channel has a limited data rate. We propose an adaptive quantization method to address this problem. A mirror descent algorithm with delayed subgradient information is established based on the theory of Bregman divergence. With a non-Euclidean Bregman projection-based scheme, the proposed method essentially generalizes many previous classical Euclidean projection-based distributed algorithms. Through the proposed adaptive quantization method, the optimal value without any quantization error can be obtained. Furthermore, comprehensive analysis on the convergence of the algorithm is carried out and our results show that the optimal convergence rate can be obtained under appropriate conditions. Finally, numerical examples are presented to demonstrate the effectiveness of our results.
在本文中，我们考虑一个在时变通信网络上具有延迟次梯度信息的分布式约束优化问题，其中每个智能体只能与其邻居进行通信，并且通信信道的数据速率有限。我们提出一种自适应量化方法来解决此问题。基于布雷格曼散度理论建立了一种具有延迟次梯度信息的镜像下降算法。通过基于非欧几里得布雷格曼投影的方案，所提出的方法本质上推广了许多先前基于经典欧几里得投影的分布式算法。通过所提出的自适应量化方法，可以获得没有任何量化误差的最优值。此外，对算法的收敛性进行了全面分析，我们的结果表明在适当条件下可以获得最优收敛速率。最后，给出数值例子以证明我们结果的有效性。
