Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems

TL;DR

This paper introduces a new decomposition framework for distributed optimization in multi-agent systems, enabling parallel, provably convergent algorithms for complex nonconvex problems in wireless communications.

Contribution

It develops the first class of inexact Jacobi best-response algorithms with convergence guarantees, and unifies various pricing schemes into a flexible, practical framework.

Findings

Algorithms outperform existing ad hoc methods

Framework includes gradient and block-coordinate descent schemes

Provides convergence guarantees for nonconvex optimization

Abstract

We propose a novel decomposition framework for the distributed optimization of general nonconvex sum-utility functions arising naturally in the system design of wireless multiuser interfering systems. Our main contributions are: i) the development of the first class of (inexact) Jacobi best-response algorithms with provable convergence, where all the users simultaneously and iteratively solve a suitably convexified version of the original sum-utility optimization problem; ii) the derivation of a general dynamic pricing mechanism that provides a unified view of existing pricing schemes that are based, instead, on heuristics; and iii) a framework that can be easily particularized to well-known applications, giving rise to very efficient practical (Jacobi or Gauss-Seidel) algorithms that outperform existing adhoc methods proposed for very specific problems. Interestingly, our framework contains as special cases well-known gradient algorithms for nonconvex sum-utility problems, and many blockcoordinate descent schemes for convex functions.