Quantized Primal-Dual Algorithms for Network Optimization with Linear Convergence

TL;DR

This paper introduces a quantized primal-dual algorithm for network optimization that ensures linear convergence under finite bandwidth constraints, with a clear relation between bandwidth and convergence speed.

Contribution

It proposes an adaptive encoding-decoding scheme and a quantized primal-dual algorithm with proven linear convergence for network optimization under communication constraints.

Findings

Algorithm achieves exact tracking of optimal solutions.

Convergence rate is explicitly related to communication bandwidth.

Validated with an exponential regression example.

Abstract

This paper studies the network optimization problem about which a group of agents cooperates to minimize a global function under practical constraints of finite bandwidth communication. Particularly, we propose an adaptive encoding-decoding scheme to handle the constrained communication between agents. Based on this scheme, the continuous-time quantized distributed primal-dual (QDPD) algorithm is developed for network optimization problems. We prove that our algorithms can exactly track an optimal solution to the corresponding convex global cost function at a linear convergence rate. Furthermore, we obtain the relation between communication bandwidth and the convergence rate of QDPD algorithms. Finally, an exponential regression example is given to illustrate our results.