Distributed Aggregative Optimization over Multi-Agent Networks

TL;DR

This paper introduces a novel distributed aggregative optimization framework for multi-agent networks, along with a gradient tracking algorithm that guarantees linear convergence under certain conditions.

Contribution

It presents a new framework for distributed optimization where local objectives depend on the average of all agents' functions, and proposes a convergent distributed gradient tracking algorithm.

Findings

The DGT algorithm converges linearly to the optimal solution.

The framework handles strongly convex global objectives.

Numerical results support theoretical convergence claims.

Abstract

This paper proposes a new framework for distributed optimization, called distributed aggregative optimization, which allows local objective functions to be dependent not only on their own decision variables, but also on the average of summable functions of decision variables of all other agents. To handle this problem, a distributed algorithm, called distributed gradient tracking (DGT), is proposed and analyzed, where the global objective function is strongly convex, and the communication graph is balanced and strongly connected. It is shown that the algorithm can converge to the optimal variable at a linear rate. A numerical example is provided to corroborate the theoretical result.