# An Exact Quantized Decentralized Gradient Descent Algorithm

arXiv: https://arxiv.org/abs/1806.11536 · HTML: https://mlsanity.com/paper/1806.11536/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2018.

## Built on by (most cited first, 30 of 36)

- [Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradients](https://mlsanity.com/paper/2102.07053/) (2021)
- [BEER: Fast O(1/T) Rate for Decentralized Nonconvex Optimization with Communication Compression](https://mlsanity.com/paper/2201.13320/) (2022)
- [Moshpit SGD: Communication-Efficient Decentralized Training on Heterogeneous Unreliable Devices](https://mlsanity.com/paper/2103.03239/) (2021)
- [FedNew: A Communication-Efficient and Privacy-Preserving Newton-Type Method for Federated Learning](https://mlsanity.com/paper/2206.08829/) (2022)
- [On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing](https://mlsanity.com/paper/2303.10695/) (2023)
- [Federated TD Learning over Finite-Rate Erasure Channels: Linear Speedup under Markovian Sampling](https://mlsanity.com/paper/2305.08104/) (2023)
- [Asynchronous Federated Learning for Sensor Data with Concept Drift](https://mlsanity.com/paper/2109.00151/) (2021)
- [Decentralized Low-Rank Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2501.15361/) (2025)
- [Innovation Compression for Communication-efficient Distributed Optimization with Linear Convergence](https://mlsanity.com/paper/2105.06697/) (2021)
- [Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks](https://mlsanity.com/paper/2106.07243/) (2021)
- [Convergence Rates of Two-Time-Scale Gradient Descent-Ascent Dynamics for Solving Nonconvex Min-Max Problems](https://mlsanity.com/paper/2112.09579/) (2021)
- [Stochastic Approximation Beyond Gradient for Signal Processing and Machine Learning](https://mlsanity.com/paper/2302.11147/) (2023)
- [Unified Analysis of Decentralized Gradient Descent: a Contraction Mapping Framework](https://mlsanity.com/paper/2503.14353/) (2025)
- [Distributed Learning With Sparsified Gradient Differences](https://mlsanity.com/paper/2202.02491/) (2022)
- [Non-Coherent Over-the-Air Decentralized Gradient Descent](https://mlsanity.com/paper/2211.10777/) (2022)
- [Decentralized Composite Optimization with Compression](https://mlsanity.com/paper/2108.04448/) (2021)
- [Quantization enabled Privacy Protection in Decentralized Stochastic Optimization](https://mlsanity.com/paper/2208.04845/) (2022)
- [Quantization for decentralized learning under subspace constraints](https://mlsanity.com/paper/2209.07821/) (2022)
- [DoCoM: Compressed Decentralized Optimization with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2202.00255/) (2022)
- [Communication-Efficient Design for Quantized Decentralized Federated Learning](https://mlsanity.com/paper/2303.08423/) (2023)
- [Distributed Adaptive Learning Under Communication Constraints](https://mlsanity.com/paper/2112.02129/) (2021)
- [Decentralized Multi-Task Stochastic Optimization With Compressed Communications](https://mlsanity.com/paper/2112.12373/) (2021)
- [Differential error feedback for communication-efficient decentralized learning](https://mlsanity.com/paper/2406.18418/) (2024)
- [Compressed Regression over Adaptive Networks](https://mlsanity.com/paper/2304.03638/) (2023)
- [FedNMUT -- Federated Noisy Model Update Tracking Convergence Analysis](https://mlsanity.com/paper/2403.13247/) (2024)
- [Communication-Efficient Distributed SGD with Compressed Sensing](https://mlsanity.com/paper/2112.07836/) (2021)
- [On Arbitrary Compression for Decentralized Consensus and Stochastic Optimization over Directed Networks](https://mlsanity.com/paper/2204.08160/) (2022)
- [Convergence Theory of Generalized Distributed Subgradient Method with Random Quantization](https://mlsanity.com/paper/2207.10969/) (2022)
- [One Gradient Frank-Wolfe for Decentralized Online Convex and Submodular Optimization](https://mlsanity.com/paper/2210.16790/) (2022)
- [Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking](https://mlsanity.com/paper/2506.07351/) (2025)

## Abstract (arXiv)

We consider the problem of decentralized consensus optimization, where the sum of n smooth and strongly convex functions are minimized over n distributed agents that form a connected network. In particular, we consider the case that the communicated local decision variables among nodes are quantized in order to alleviate the communication bottleneck in distributed optimization. We propose the Quantized Decentralized Gradient Descent (QDGD) algorithm, in which nodes update their local decision variables by combining the quantized information received from their neighbors with their local information. We prove that under standard strong convexity and smoothness assumptions for the objective function, QDGD achieves a vanishing mean solution error under customary conditions for quantizers. To the best of our knowledge, this is the first algorithm that achieves vanishing consensus error in the presence of quantization noise. Moreover, we provide simulation results that show tight agreement between our derived theoretical convergence rate and the numerical results.