D-ADMM: A Communication-Efficient Distributed Algorithm For Separable Optimization

TL;DR

D-ADMM is a new distributed algorithm that efficiently solves separable optimization problems across networks, reducing communication costs while maintaining convergence under certain conditions, with applications in signal processing and control.

Contribution

This paper introduces D-ADMM, a communication-efficient distributed algorithm for separable optimization, with proven convergence and practical effectiveness in various signal processing tasks.

Findings

D-ADMM converges under bipartite network or strong convexity conditions.

D-ADMM requires less communication than existing algorithms.

Effective in applications like consensus, compressed sensing, SVMs.

Abstract

We propose a distributed algorithm, named Distributed Alternating Direction Method of Multipliers (D-ADMM), for solving separable optimization problems in networks of interconnected nodes or agents. In a separable optimization problem there is a private cost function and a private constraint set at each node. The goal is to minimize the sum of all the cost functions, constraining the solution to be in the intersection of all the constraint sets. D-ADMM is proven to converge when the network is bipartite or when all the functions are strongly convex, although in practice, convergence is observed even when these conditions are not met. We use D-ADMM to solve the following problems from signal processing and control: average consensus, compressed sensing, and support vector machines. Our simulations show that D-ADMM requires less communications than state-of-the-art algorithms to achieve a given accuracy level. Algorithms with low communication requirements are important, for example, in sensor networks, where sensors are typically battery-operated and communicating is the most energy consuming operation.