# IDEAL: Inexact DEcentralized Accelerated Augmented Lagrangian Method

arXiv: https://arxiv.org/abs/2006.06733 · HTML: https://mlsanity.com/paper/2006.06733/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

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

- [Cross-Gradient Aggregation for Decentralized Learning from Non-IID data](https://mlsanity.com/paper/2103.02051/) (2021)
- [Accelerated Primal-Dual Gradient Method for Smooth and Convex-Concave Saddle-Point Problems with Bilinear Coupling](https://mlsanity.com/paper/2112.15199/) (2021)
- [Accelerated Gradient Tracking over Time-varying Graphs for Decentralized Optimization](https://mlsanity.com/paper/2104.02596/) (2021)
- [Decentralized Inexact Proximal Gradient Method With Network-Independent Stepsizes for Convex Composite Optimization](https://mlsanity.com/paper/2302.03238/) (2023)
- [DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networks](https://mlsanity.com/paper/2511.12836/) (2025)
- [Decentralized Proximal Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2605.00723/) (2026)

## Abstract (arXiv)

We introduce a framework for designing primal methods under the decentralized optimization setting where local functions are smooth and strongly convex. Our approach consists of approximately solving a sequence of sub-problems induced by the accelerated augmented Lagrangian method, thereby providing a systematic way for deriving several well-known decentralized algorithms including EXTRA arXiv:1404.6264 and SSDA arXiv:1702.08704. When coupled with accelerated gradient descent, our framework yields a novel primal algorithm whose convergence rate is optimal and matched by recently derived lower bounds. We provide experimental results that demonstrate the effectiveness of the proposed algorithm on highly ill-conditioned problems.