# Distributed Online Convex Optimization with an Aggregative Variable

arXiv: https://arxiv.org/abs/2007.06844 · HTML: https://mlsanity.com/paper/2007.06844/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2020.

## Built on by (most cited first, 7 of 7)

- [Regret and Cumulative Constraint Violation Analysis for Distributed Online Constrained Convex Optimization](https://mlsanity.com/paper/2105.00321/) (2021)
- [Online Federated Learning via Non-Stationary Detection and Adaptation amidst Concept Drift](https://mlsanity.com/paper/2211.12578/) (2022)
- [Gradient and Projection Free Distributed Online Min-Max Resource Optimization](https://mlsanity.com/paper/2112.03896/) (2021)
- [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022)
- [Learning-Augmented Decentralized Online Convex Optimization in Networks](https://mlsanity.com/paper/2306.10158/) (2023)
- [Accelerated Distributed Aggregative Optimization](https://mlsanity.com/paper/2304.08051/) (2023)
- [A Hybrid Stochastic Gradient Tracking Method for Distributed Online Optimization Over Time-Varying Directed Networks](https://mlsanity.com/paper/2508.20645/) (2025)

## Abstract (arXiv)

This paper investigates distributed online convex optimization in the presence of an aggregative variable without any global/central coordinators over a multi-agent network, where each individual agent is only able to access partial information of time-varying global loss functions, thus requiring local information exchanges between neighboring agents. Motivated by many applications in reality, the considered local loss functions depend not only on their own decision variables, but also on an aggregative variable, such as the average of all decision variables. To handle this problem, an Online Distributed Gradient Tracking algorithm (O-DGT) is proposed with exact gradient information and it is shown that the dynamic regret is upper bounded by three terms: a sublinear term, a path variation term, and a gradient variation term. Meanwhile, the O-DGT algorithm is also analyzed with stochastic/noisy gradients, showing that the expected dynamic regret has the same upper bound as the exact gradient case. To our best knowledge, this paper is the first to study online convex optimization in the presence of an aggregative variable, which enjoys new characteristics in comparison with the conventional scenario without the aggregative variable. Finally, a numerical experiment is provided to corroborate the obtained theoretical results.