# Q-GADMM: Quantized Group ADMM for Communication Efficient Decentralized Machine Learning

arXiv: https://arxiv.org/abs/1910.10453 · HTML: https://mlsanity.com/paper/1910.10453/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2019.

## Built on by (most cited first, 17 of 17)

- [FedNew: A Communication-Efficient and Privacy-Preserving Newton-Type Method for Federated Learning](https://mlsanity.com/paper/2206.08829/) (2022)
- [Improved Communication Efficiency in Federated Natural Policy Gradient via ADMM-based Gradient Updates](https://mlsanity.com/paper/2310.19807/) (2023)
- [Asynchronous Federated Reinforcement Learning with Policy Gradient Updates: Algorithm Design and Convergence Analysis](https://mlsanity.com/paper/2404.08003/) (2024)
- [Wireless Quantized Federated Learning: A Joint Computation and Communication Design](https://mlsanity.com/paper/2203.05878/) (2022)
- [Federated Learning and Meta Learning: Approaches, Applications, and Directions](https://mlsanity.com/paper/2210.13111/) (2022)
- [Distributed Learning With Sparsified Gradient Differences](https://mlsanity.com/paper/2202.02491/) (2022)
- [Rendering Wireless Environments Useful for Gradient Estimators: A Zero-Order Stochastic Federated Learning Method](https://mlsanity.com/paper/2401.17460/) (2024)
- [Distributed Learning based on 1-Bit Gradient Coding in the Presence of Stragglers](https://mlsanity.com/paper/2403.14716/) (2024)
- [Learning, Computing, and Trustworthiness in Intelligent IoT Environments: Performance-Energy Tradeoffs](https://mlsanity.com/paper/2110.01686/) (2021)
- [Rate-Constrained Quantization for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2409.06319/) (2024)
- [Scaling up Stochastic Gradient Descent for Non-convex Optimisation](https://mlsanity.com/paper/2210.02882/) (2022)
- [Communication and Energy Efficient Federated Learning using Zero-Order Optimization Technique](https://mlsanity.com/paper/2409.16456/) (2024)
- [Communication-Efficient Zero-Order and First-Order Federated Learning Methods over Wireless Networks](https://mlsanity.com/paper/2508.08013/) (2025)
- [Decentralized Optimization with Topology-Independent Communication](https://mlsanity.com/paper/2509.14488/) (2025)
- [Generalized ADMM in Distributed Learning via Variational Inequality](https://mlsanity.com/paper/2104.12608/) (2021)
- [Federated Learning for Energy Constrained IoT devices: A systematic mapping study](https://mlsanity.com/paper/2301.03720/) (2023)
- [Distributed Linear Regression with Compositional Covariates](https://mlsanity.com/paper/2310.13969/) (2023)

## Abstract (arXiv)

In this article, we propose a communication-efficient decentralized machine learning (ML) algorithm, coined quantized group ADMM (Q-GADMM). To reduce the number of communication links, every worker in Q-GADMM communicates only with two neighbors, while updating its model via the group alternating direction method of multipliers (GADMM). Moreover, each worker transmits the quantized difference between its current model and its previously quantized model, thereby decreasing the communication payload size. However, due to the lack of centralized entity in decentralized ML, the spatial sparsity and payload compression may incur error propagation, hindering model training convergence. To overcome this, we develop a novel stochastic quantization method to adaptively adjust model quantization levels and their probabilities, while proving the convergence of Q-GADMM for convex objective functions. Furthermore, to demonstrate the feasibility of Q-GADMM for non-convex and stochastic problems, we propose quantized stochastic GADMM (Q-SGADMM) that incorporates deep neural network architectures and stochastic sampling. Simulation results corroborate that Q-GADMM significantly outperforms GADMM in terms of communication efficiency while achieving the same accuracy and convergence speed for a linear regression task. Similarly, for an image classification task using DNN, Q-SGADMM achieves significantly less total communication cost with identical accuracy and convergence speed compared to its counterpart without quantization, i.e., stochastic GADMM (SGADMM).