# A Compressed Gradient Tracking Method for Decentralized Optimization with Linear Convergence

arXiv: https://arxiv.org/abs/2205.12623 · HTML: https://mlsanity.com/paper/2205.12623/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2022.

## Built on by (most cited first, 9 of 9)

- [Non-Coherent Over-the-Air Decentralized Gradient Descent](https://mlsanity.com/paper/2211.10777/) (2022)
- [CEDAS: A Compressed Decentralized Stochastic Gradient Method with Improved Convergence](https://mlsanity.com/paper/2301.05872/) (2023)
- [Log-Scale Quantization in Distributed First-Order Methods: Gradient-based Learning from Distributed Data](https://mlsanity.com/paper/2406.00621/) (2024)
- [Decentralized Optimization with Topology-Independent Communication](https://mlsanity.com/paper/2509.14488/) (2025)
- [A Communication and Computation Efficient Fully First-order Method for Decentralized Bilevel Optimization](https://mlsanity.com/paper/2410.14115/) (2024)
- [Gradient Purification: Defense Against Poisoning Attack in Decentralized Federated Learning](https://mlsanity.com/paper/2501.04453/) (2025)
- [A Hybrid Stochastic Gradient Tracking Method for Distributed Online Optimization Over Time-Varying Directed Networks](https://mlsanity.com/paper/2508.20645/) (2025)
- [Decentralized Stochastic Subgradient-type Methods with Communication Compression for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2607.01755/) (2026)
- [Decentralized Gradient Descent: Bottleneck Regimes and Budget Complexity](https://mlsanity.com/paper/2607.12172/) (2026)

## Abstract (arXiv)

Communication compression techniques are of growing interests for solving the decentralized optimization problem under limited communication, where the global objective is to minimize the average of local cost functions over a multi-agent network using only local computation and peer-to-peer communication. In this paper, we propose a novel compressed gradient tracking algorithm (C-GT) that combines gradient tracking technique with communication compression. In particular, C-GT is compatible with a general class of compression operators that unifies both unbiased and biased compressors. We show that C-GT inherits the advantages of gradient tracking-based algorithms and achieves linear convergence rate for strongly convex and smooth objective functions. Numerical examples complement the theoretical findings and demonstrate the efficiency and flexibility of the proposed algorithm.