# A Canonical Form for First-Order Distributed Optimization Algorithms

arXiv: https://arxiv.org/abs/1809.08709 · HTML: https://mlsanity.com/paper/1809.08709/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2018.

## Built on by (most cited first, 2 of 2)

- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [A Tight Theory of Error Feedback Algorithms in Distributed Optimization](https://mlsanity.com/paper/2605.31594/) (2026)

## Abstract (arXiv)

We consider the distributed optimization problem in which a network of agents aims to minimize the average of local functions. To solve this problem, several algorithms have recently been proposed where agents perform various combinations of communication with neighbors, local gradient computations, and updates to local state variables. In this paper, we present a canonical form that characterizes any first-order distributed algorithm that can be implemented using a single round of communication and gradient computation per iteration, and where each agent stores up to two state variables. The canonical form features a minimal set of parameters that are both unique and expressive enough to capture any distributed algorithm in this class. The generic nature of our canonical form enables the systematic analysis and design of distributed optimization algorithms.