# Quantized Distributed Gradient Tracking Algorithm with Linear Convergence in Directed Networks

arXiv: https://arxiv.org/abs/2104.03649 · HTML: https://mlsanity.com/paper/2104.03649/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2021.

## Built on by (most cited first, 8 of 8)

- [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)
- [CEDAS: A Compressed Decentralized Stochastic Gradient Method with Improved Convergence](https://mlsanity.com/paper/2301.05872/) (2023)
- [Decentralized Composite Optimization with Compression](https://mlsanity.com/paper/2108.04448/) (2021)
- [Log-Scale Quantization in Distributed First-Order Methods: Gradient-based Learning from Distributed Data](https://mlsanity.com/paper/2406.00621/) (2024)
- [Locally Differentially Private Gradient Tracking for Distributed Online Learning over Directed Graphs](https://mlsanity.com/paper/2310.16105/) (2023)
- [Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking](https://mlsanity.com/paper/2506.07351/) (2025)
- [Compressed Proximal Federated Learning for Non-Convex Composite Optimization on Heterogeneous Data](https://mlsanity.com/paper/2603.07654/) (2026)

## Abstract (arXiv)

Communication efficiency is a major bottleneck in the applications of distributed networks. To address the problem, the problem of quantized distributed optimization has attracted a lot of attention. However, most of the existing quantized distributed optimization algorithms can only converge sublinearly. To achieve linear convergence, this paper proposes a novel quantized distributed gradient tracking algorithm (Q-DGT) to minimize a finite sum of local objective functions over directed networks. Moreover, we explicitly derive the update rule for the number of quantization levels, and prove that Q-DGT can converge linearly even when the exchanged variables are respectively one bit. Numerical results also confirm the efficiency of the proposed algorithm.