# Distributed and Inexact Proximal Gradient Method for Online Convex Optimization

arXiv: https://arxiv.org/abs/2001.00870 · HTML: https://mlsanity.com/paper/2001.00870/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2020.

## Built on by (most cited first, 6 of 6)

- [Enhancing Privacy in Federated Learning through Local Training](https://mlsanity.com/paper/2403.17572/) (2024)
- [Distributed Online Non-convex Optimization with Composite Regret](https://mlsanity.com/paper/2209.10105/) (2022)
- [Robust Online Learning over Networks](https://mlsanity.com/paper/2309.00520/) (2023)
- [A Survey on Distributed Online Optimization and Game](https://mlsanity.com/paper/2205.00473/) (2022)
- [Online Distributed Learning with Quantized Finite-Time Coordination](https://mlsanity.com/paper/2307.06620/) (2023)
- [Personalized and Resilient Distributed Learning Through Opinion Dynamics](https://mlsanity.com/paper/2505.14081/) (2025)

## Abstract (arXiv)

This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function and a non-smooth convex function, both changing over time. By coordinating through a connected communication network, the nodes collaboratively track the trajectory of the minimizers without exchanging their local cost functions. The DPGM is implemented in an online fashion, that is, in a setting where only a limited number of steps are implemented before the function changes. Moreover, the algorithm is analyzed in an inexact scenario, that is, with a source of additive noise, that can represent e.g. communication noise or quantization. It is shown that the tracking error of the online inexact DPGM is upper-bounded by a convergent linear system, guaranteeing convergence within a neighborhood of the optimal solution.