# An Asynchronous Distributed Proximal Gradient Method for Composite Convex Optimization

arXiv: https://arxiv.org/abs/1409.8547 · HTML: https://mlsanity.com/paper/1409.8547/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2014.

## Built on by (most cited first, 4 of 4)

- [Distributed Learning Systems with First-order Methods](https://mlsanity.com/paper/2104.05245/) (2021)
- [Towards Demystifying Serverless Machine Learning Training](https://mlsanity.com/paper/2105.07806/) (2021)
- [Asynchronous Federated Learning for Sensor Data with Concept Drift](https://mlsanity.com/paper/2109.00151/) (2021)
- [Distributed Optimization via Kernelized Multi-armed Bandits](https://mlsanity.com/paper/2312.04719/) (2023)

## Abstract (arXiv)

We propose a distributed first-order augmented Lagrangian (DFAL) algorithm to minimize the sum of composite convex functions, where each term in the sum is a private cost function belonging to a node, and only nodes connected by an edge can directly communicate with each other. This optimization model abstracts a number of applications in distributed sensing and machine learning. We show that any limit point of DFAL iterates is optimal; and for any ε>0, an ε-optimal and ε-feasible solution can be computed within O(log(ε-1)) DFAL iterations, which require O(fracpsimax1.5dmin ε-1) proximal gradient computations and communications per node in total, where psimax denotes the largest eigenvalue of the graph Laplacian, and dmin is the minimum degree of the graph. We also propose an asynchronous version of DFAL by incorporating randomized block coordinate descent methods; and demonstrate the efficiency of DFAL on large scale sparse-group LASSO problems.