Quantized Primal-Dual Algorithms for Network Optimization With Linear Convergence

This note investigates a network optimization problem in which a group of agents cooperate to minimize a global function under the practical constraint of finite-bandwidth communication. We propose an adaptive encoding-decoding scheme to handle the quantization communication between agents. Based on this scheme, we develop a continuous-time quantized distributed primal-dual algorithm for the network optimization problem. Our algorithm achieves linear convergence to an exact optimal solution. Furthermore, we obtain the relationship between the communication bandwidth and the convergence rate. Finally, we use a distributed logistic regression problem to illustrate the effectiveness of our methods.