Distributed Cross-Layer Optimization in Wireless Networks: A Second-Order Approach

TL;DR

This paper introduces a second-order distributed optimization method for wireless networks, achieving faster convergence than traditional first-order methods by developing a decentralized Hessian inverse computation approach.

Contribution

It presents the first distributed Newton's method for wireless networks, overcoming interference challenges with novel Hessian inverse computation techniques.

Findings

Achieves quadratic convergence rate in distributed wireless network optimization.

Derives closed-form Hessian inverse for fully interfering links.

Proposes iterative scheme for general interference scenarios.

Abstract

Due to the rapidly growing scale and heterogeneity of wireless networks, the design of distributed cross-layer optimization algorithms have received significant interest from the networking research community. So far, the standard distributed cross-layer approach in the literature is based on first-order Lagrangian dual decomposition and the subgradient method, which suffers a slow convergence rate. In this paper, we make the first known attempt to develop a distributed Newton's method, which is second-order and enjoys a quadratic convergence rate. However, due to interference in wireless networks, the Hessian matrix of the cross-layer problem has an non-separable structure. As a result, developing a distributed second-order algorithm is far more challenging than its counterpart for wireline networks. Our main results in this paper are two-fold: i) For a special network setting where all links mutually interfere, we derive decentralized closed-form expressions to compute the Hessian inverse; ii) For general wireless networks where the interference relationships are arbitrary, we propose a distributed iterative matrix splitting scheme for the Hessian inverse. These results successfully lead to a new theoretical framework for cross-layer optimization in wireless networks. More importantly, our work contributes to an exciting second-order paradigm shift in wireless networks optimization theory.