# Accelerated Distributed Aggregative Optimization

arXiv: https://arxiv.org/abs/2304.08051 · HTML: https://mlsanity.com/paper/2304.08051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 17 Apr 2023.

## Builds on (most cited first, 15 of 15)

- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [On the Convergence of Decentralized Gradient Descent](https://mlsanity.com/paper/1310.7063/) (2013)
- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [Topology-aware Generalization of Decentralized SGD](https://mlsanity.com/paper/2206.12680/) (2022)
- [Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning](https://mlsanity.com/paper/1402.4419/) (2014)
- [Accelerated Distributed Nesterov Gradient Descent](https://mlsanity.com/paper/1705.07176/) (2017)
- [A linear algorithm for optimization over directed graphs with geometric convergence](https://mlsanity.com/paper/1803.02503/) (2018)
- [Distributed heavy-ball: A generalization and acceleration of first-order methods with gradient tracking](https://mlsanity.com/paper/1808.02942/) (2018)
- [Distributed Online Convex Optimization with an Aggregative Variable](https://mlsanity.com/paper/2007.06844/) (2020)
- [Distributed Nesterov gradient methods over arbitrary graphs](https://mlsanity.com/paper/1901.06995/) (2019)
- [Distributed Algorithms for Aggregative Games on Graphs](https://mlsanity.com/paper/1605.00267/) (2016)
- [Distributed Aggregative Optimization over Multi-Agent Networks](https://mlsanity.com/paper/2005.13436/) (2020)
- [Distributed Online Aggregative Optimization for Dynamic Multi-robot Coordination](https://mlsanity.com/paper/2104.09847/) (2021)
- [Distributed aggregative optimization with quantization communication](https://mlsanity.com/paper/2201.01969/) (2022)
- [Distributed Projection-free Algorithm for Constrained Aggregative Optimization](https://mlsanity.com/paper/2207.11885/) (2022)

## Abstract (arXiv)

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 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.