Accelerated Distributed Aggregative Optimization

TL;DR

This paper introduces two accelerated algorithms, DAGT-HB and DAGT-NES, for distributed aggregative optimization, achieving faster convergence rates by combining momentum methods with gradient tracking.

Contribution

The paper proposes novel accelerated algorithms for distributed aggregative optimization that guarantee global linear convergence under certain conditions.

Findings

Algorithms converge at a global R-linear rate.

Numerical experiments confirm effectiveness and superiority.

Methods outperform existing approaches in speed.

Abstract

In this paper, we investigate a distributed aggregative optimization problem in a network, where each agent has its own local cost function which depends not only on the local state variable but also on an aggregated function of state variables from all agents. To accelerate the optimization process, we combine heavy ball and Nesterov's accelerated methods with distributed aggregative gradient tracking, and propose two novel algorithms named DAGT-HB and DAGT-NES for solving the distributed aggregative optimization problem. We analyse that the DAGT-HB and DAGT-NES algorithms can converge to an optimal solution at a global $\mathbf{R}-$linear convergence rate when the objective function is smooth and strongly convex, and when the parameters (e.g., step size and momentum coefficients) are selected within certain ranges. A numerical experiment on the optimal placement problem is given to verify the effectiveness and superiority of our proposed algorithms.