Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization

TL;DR

This paper introduces a novel network optimization algorithm that achieves rapid convergence, minimal delay, and simple implementation, addressing longstanding challenges in distributed network optimization.

Contribution

It proposes a new algorithmic framework based on an inexact Uzawa method that ensures optimal utility, fast convergence, and low delay without complex per-flow information.

Findings

Converges in O(log(1/ε)) iterations, faster than existing algorithms.

Guarantees finite queue length for optimal utility.

Provides a new theoretical proof of global linear convergence without full rank assumptions.

Abstract

Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality, convergence speed, and delay. To address these challenges, in this paper, we propose a new algorithmic framework with all these metrics approaching optimality. The salient features of our new algorithm are three-fold: (i) fast convergence: it converges with only $O(\log(1/\epsilon))$ iterations that is the fastest speed among all the existing algorithms; (ii) low delay: it guarantees optimal utility with finite queue length; (iii) simple implementation: the control variables of this algorithm are based on virtual queues that do not require maintaining per-flow information. The new technique builds on a kind of inexact Uzawa method in the Alternating Directional Method of Multiplier, and provides a new theoretical path to prove global and linear convergence rate of such a method without requiring the full rank assumption of the constraint matrix.