# A Distributed Flexible Delay-tolerant Proximal Gradient Algorithm

arXiv: https://arxiv.org/abs/1806.09429 · HTML: https://mlsanity.com/paper/1806.09429/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2018.

## Built on by (most cited first, 3 of 3)

- [Asynchronous Iterations in Optimization: New Sequence Results and Sharper Algorithmic Guarantees](https://mlsanity.com/paper/2109.04522/) (2021)
- [Review of Mathematical Optimization in Federated Learning](https://mlsanity.com/paper/2412.01630/) (2024)
- [On Parallel or Distributed Asynchronous Iterations with Unbounded Delays and Possible Out of Order Messages or Flexible Communication for Convex Optimization Problems and Machine Learning](https://mlsanity.com/paper/2210.04626/) (2022)

## Abstract (arXiv)

We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed algorithm is adjustable to various levels of communication cost, delays, machines computational power, and functions smoothness. A unique feature is that the stepsizes do not depend on communication delays nor number of machines, which is highly desirable for scalability. We prove that the algorithm converges linearly in the strongly convex case, and provide guarantees of convergence for the non-strongly convex case. The obtained rates are the same as the vanilla proximal gradient algorithm over some introduced epoch sequence that subsumes the delays of the system. We provide numerical results on large-scale machine learning problems to demonstrate the merits of the proposed method.