Distributed Partitioned Big-Data Optimization via Asynchronous Dual Decomposition

TL;DR

This paper introduces an asynchronous distributed optimization algorithm for large-scale, sparse, partitioned problems in peer-to-peer networks, improving scalability and reducing redundancy by leveraging problem structure.

Contribution

It proposes a novel asynchronous dual decomposition method that partitions the decision variables among nodes, enhancing efficiency in distributed big-data optimization.

Findings

Algorithm achieves scalable distributed optimization

Reduces redundant information sharing

Exploits problem sparsity for efficiency

Abstract

In this paper we consider a novel partitioned framework for distributed optimization in peer-to-peer networks. In several important applications the agents of a network have to solve an optimization problem with two key features: (i) the dimension of the decision variable depends on the network size, and (ii) cost function and constraints have a sparsity structure related to the communication graph. For this class of problems a straightforward application of existing consensus methods would show two inefficiencies: poor scalability and redundancy of shared information. We propose an asynchronous distributed algorithm, based on dual decomposition and coordinate methods, to solve partitioned optimization problems. We show that, by exploiting the problem structure, the solution can be partitioned among the nodes, so that each node just stores a local copy of a portion of the decision variable (rather than a copy of the entire decision vector) and solves a small-scale local problem.