# Geometrically Convergent Distributed Optimization with Uncoordinated Step-Sizes

arXiv: https://arxiv.org/abs/1609.05877 · HTML: https://mlsanity.com/paper/1609.05877/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2016.

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

- [An Improved Analysis of Gradient Tracking for Decentralized Machine Learning](https://mlsanity.com/paper/2202.03836/) (2022)
- [Decentralized Stochastic Optimization with Inherent Privacy Protection](https://mlsanity.com/paper/2205.03884/) (2022)
- [DISA: A Dual Inexact Splitting Algorithm for Distributed Convex Composite Optimization](https://mlsanity.com/paper/2209.01850/) (2022)
- [Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimization](https://mlsanity.com/paper/2302.03238/) (2023)
- [Decentralized Federated Learning with Gradient Tracking over Time-Varying Directed Networks](https://mlsanity.com/paper/2409.17189/) (2024)
- [MUSIC: Accelerated Convergence for Distributed Optimization With Inexact and Exact Methods](https://mlsanity.com/paper/2403.02589/) (2024)
- [Local adapt-then-combine algorithms for distributed nonsmooth optimization: Achieving provable communication acceleration](https://mlsanity.com/paper/2602.16148/) (2026)

## Abstract (arXiv)

A recent algorithmic family for distributed optimization, DIGing's, have been shown to have geometric convergence over time-varying undirected/directed graphs. Nevertheless, an identical step-size for all agents is needed. In this paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation of the DIGing algorithm under uncoordinated step-sizes. We show that the ATC variation of DIGing algorithm converges geometrically fast even if the step-sizes are different among the agents. In addition, our analysis implies that the ATC structure can accelerate convergence compared to the distributed gradient descent (DGD) structure which has been used in the original DIGing algorithm.