Convergence Analysis of Quantized Primal-Dual Algorithms in Network Utility Maximization Problems
By Ehsan Nekouei, Tansu Alpcan, G. Nair, R. Evans. 2016
12 citations recorded by the source corpus.
This paper investigates the asymptotic and nonasymptotic behavior of the quantized primal-dual (PD) algorithm in network utility maximization (NUM) problems, in which a group of agents maximizes the sum of their individual concave objective functions under linear constraints. In the asymptotic scenario, we use the information-theoretic notion of differential entropy power to establish universal bounds on the maximum exponential convergence rates of joint PD, primal and dual variables under optimum-achieving quantization schemes. These results provide tradeoffs between the speed of exponential convergence, the agents' objective functions, the communication bit rates, and the number of agents and constraints. In the nonasymptotic scenario, we obtain lower bounds on the mean square distance of joint PD, primal and dual variables from the optimal solution at any time instant. These bounds hold regardless of the quantization scheme used.
Subfields: Computer Networks and Communications, Electrical and Electronic Engineering
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In Computer Networks and Communications
In Electrical and Electronic Engineering
- H. Vincent Poor
- Howard H. Yang
- Tony Q. S. Quek
- Zuozhu Liu
- Zhiguo Ding
- Mingzhe Chen
- Walid Saad
- Yuanwei Liu
Citations in the corpus
- Scheduling Policies for Federated Learning in Wireless Networks (2019, background): “As such, reducing the dimension of the updated parameters via compression or quantization [36] so as to maintain a relatively small decoding threshold at the AP side is important to improve the convergence rate of FL in wireless networks.”