# Distributed Fixed Point Methods with Compressed Iterates

arXiv: https://arxiv.org/abs/1912.09925 · HTML: https://mlsanity.com/paper/1912.09925/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2019.

## Built on by (most cited first, 11 of 11)

- [DoCoFL: Downlink Compression for Cross-Device Federated Learning](https://mlsanity.com/paper/2302.00543/) (2023)
- [Partial Variable Training for Efficient On-Device Federated Learning](https://mlsanity.com/paper/2110.05607/) (2021)
- [Federated Random Reshuffling with Compression and Variance Reduction](https://mlsanity.com/paper/2205.03914/) (2022)
- [Improving Accelerated Federated Learning with Compression and Importance Sampling](https://mlsanity.com/paper/2306.03240/) (2023)
- [Online Model Compression for Federated Learning with Large Models](https://mlsanity.com/paper/2205.03494/) (2022)
- [Shifted Compression Framework: Generalizations and Improvements](https://mlsanity.com/paper/2206.10452/) (2022)
- [Personalized Federated Learning with Communication Compression](https://mlsanity.com/paper/2209.05148/) (2022)
- [Towards a Better Theoretical Understanding of Independent Subnetwork Training](https://mlsanity.com/paper/2306.16484/) (2023)
- [Local Methods with Adaptivity via Scaling](https://mlsanity.com/paper/2406.00846/) (2024)
- [Tight analyses of first-order methods with error feedback](https://mlsanity.com/paper/2506.05271/) (2025)
- [First Provable Guarantees for Practical Private FL: Beyond Restrictive Assumptions](https://mlsanity.com/paper/2512.21521/) (2025)

## Abstract (arXiv)

We propose basic and natural assumptions under which iterative optimization methods with compressed iterates can be analyzed. This problem is motivated by the practice of federated learning, where a large model stored in the cloud is compressed before it is sent to a mobile device, which then proceeds with training based on local data. We develop standard and variance reduced methods, and establish communication complexity bounds. Our algorithms are the first distributed methods with compressed iterates, and the first fixed point methods with compressed iterates.