# Communication-Efficient Zero-Order and First-Order Federated Learning Methods over Wireless Networks

arXiv: https://arxiv.org/abs/2508.08013 · HTML: https://mlsanity.com/paper/2508.08013/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 35 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Builds on (most cited first, 25 of 25)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [A Primer on Zeroth-Order Optimization in Signal Processing and Machine Learning](https://mlsanity.com/paper/2006.06224/) (2020)
- [FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Data](https://mlsanity.com/paper/2005.11418/) (2020)
- [Distributed Learning with Compressed Gradient Differences](https://mlsanity.com/paper/1901.09269/) (2019)
- [LAG: Lazily Aggregated Gradient for Communication-Efficient Distributed Learning](https://mlsanity.com/paper/1805.09965/) (2018)
- [FedDANE: A Federated Newton-Type Method](https://mlsanity.com/paper/2001.01920/) (2020)
- [Communication-Efficient Stochastic Zeroth-Order Optimization for Federated Learning](https://mlsanity.com/paper/2201.09531/) (2022)
- [Distributed learning with compressed gradients](https://mlsanity.com/paper/1806.06573/) (2018)
- [Communication-Efficient Adaptive Federated Learning](https://mlsanity.com/paper/2205.02719/) (2022)
- [FedNew: A Communication-Efficient and Privacy-Preserving Newton-Type Method for Federated Learning](https://mlsanity.com/paper/2206.08829/) (2022)
- [Just One Byte (per gradient): A Note on Low-Bandwidth Decentralized Language Model Finetuning Using Shared Randomness](https://mlsanity.com/paper/2306.10015/) (2023)
- [Q-GADMM: Quantized Group ADMM for Communication Efficient Decentralized Machine Learning](https://mlsanity.com/paper/1910.10453/) (2019)
- [BAFFLE: A Baseline of Backpropagation-Free Federated Learning](https://mlsanity.com/paper/2301.12195/) (2023)
- [Distributed Learning With Sparsified Gradient Differences](https://mlsanity.com/paper/2202.02491/) (2022)
- [Zeroth and First Order Stochastic Frank-Wolfe Algorithms for Constrained Optimization](https://mlsanity.com/paper/2107.06534/) (2021)
- [Rendering Wireless Environments Useful for Gradient Estimators: A Zero-Order Stochastic Federated Learning Method](https://mlsanity.com/paper/2401.17460/) (2024)
- [Lazy Queries Can Reduce Variance in Zeroth-order Optimization](https://mlsanity.com/paper/2206.07126/) (2022)
- [Communication and Energy Efficient Federated Learning using Zero-Order Optimization Technique](https://mlsanity.com/paper/2409.16456/) (2024)

## Built on by (most cited first, 1 of 1)

- [Privacy-Enhanced Zero-Order Federated Learning via xMK-CKKS over Wireless Channels](https://mlsanity.com/paper/2605.30123/) (2026)

## Abstract (arXiv)

Federated Learning (FL) is an emerging learning framework that enables edge devices to collaboratively train ML models without sharing their local data. FL faces, however, a significant challenge due to the high amount of information that must be exchanged between the devices and the aggregator in the training phase, which can exceed the limited capacity of wireless systems. In this paper, two communication-efficient FL methods are considered where communication overhead is reduced by communicating scalar values instead of long vectors and by allowing high number of users to send information simultaneously. The first approach employs a zero-order optimization technique with two-point gradient estimator, while the second involves a first-order gradient computation strategy. The novelty lies in leveraging channel information in the learning algorithms, eliminating hence the need for additional resources to acquire channel state information (CSI) and to remove its impact, as well as in considering asynchronous devices. We provide a rigorous analytical framework for the two methods, deriving convergence guarantees and establishing appropriate performance bounds.