# Rendering Wireless Environments Useful for Gradient Estimators: A Zero-Order Stochastic Federated Learning Method

arXiv: https://arxiv.org/abs/2401.17460 · HTML: https://mlsanity.com/paper/2401.17460/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 42 references that are in the map.
- First posted on arXiv 30 Jan 2024.

## Builds on (most cited first, 29 of 29)

- [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)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Black-box Adversarial Attacks with Limited Queries and Information](https://mlsanity.com/paper/1804.08598/) (2018)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [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)
- [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)
- [Federated Bayesian Optimization via Thompson Sampling](https://mlsanity.com/paper/2010.10154/) (2020)
- [ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization](https://mlsanity.com/paper/1910.06513/) (2019)
- [FedDANE: A Federated Newton-Type Method](https://mlsanity.com/paper/2001.01920/) (2020)
- [Over-the-Air Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2009.12787/) (2020)
- [Convergence of Update Aware Device Scheduling for Federated Learning at the Wireless Edge](https://mlsanity.com/paper/2001.10402/) (2020)
- [Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems](https://mlsanity.com/paper/1812.08305/) (2018)
- [On Analog Gradient Descent Learning over Multiple Access Fading Channels](https://mlsanity.com/paper/1908.07463/) (2019)
- [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)
- [Model Agnostic Contrastive Explanations for Structured Data](https://mlsanity.com/paper/1906.00117/) (2019)
- [Dynamic Scheduling for Over-the-Air Federated Edge Learning with Energy Constraints](https://mlsanity.com/paper/2106.00490/) (2021)
- [Contrasting Exploration in Parameter and Action Space: A Zeroth-Order Optimization Perspective](https://mlsanity.com/paper/1901.11503/) (2019)
- [FedNew: A Communication-Efficient and Privacy-Preserving Newton-Type Method for Federated Learning](https://mlsanity.com/paper/2206.08829/) (2022)
- [Q-GADMM: Quantized Group ADMM for Communication Efficient Decentralized Machine Learning](https://mlsanity.com/paper/1910.10453/) (2019)
- [Making Cell-Free Massive MIMO Competitive With MMSE Processing and Centralized Implementation](https://mlsanity.com/paper/1903.10611/) (2019)
- [Distributed Learning With Sparsified Gradient Differences](https://mlsanity.com/paper/2202.02491/) (2022)
- [Zero-Order One-Point Estimate with Distributed Stochastic Gradient-Tracking Technique](https://mlsanity.com/paper/2210.05618/) (2022)

## Built on by (most cited first, 4 of 4)

- [Communication and Energy Efficient Federated Learning using Zero-Order Optimization Technique](https://mlsanity.com/paper/2409.16456/) (2024)
- [Fed-ZOE: Communication-Efficient Over-the-Air Federated Learning via Zeroth-Order Estimation](https://mlsanity.com/paper/2412.16779/) (2024)
- [Communication-Efficient Zero-Order and First-Order Federated Learning Methods over Wireless Networks](https://mlsanity.com/paper/2508.08013/) (2025)
- [AirGC-CD: Gaussian-Circulant Precoding for Exactly Debiasable PAPR Reduction in Over-the-Air Federated Learning](https://mlsanity.com/paper/2609.23084/) (2026)

## Abstract (arXiv)

Cross-device federated learning (FL) is a growing machine learning setting whereby multiple edge devices collaborate to train a model without disclosing their raw data. With the great number of mobile devices participating in more FL applications via the wireless environment, the practical implementation of these applications will be hindered due to the limited uplink capacity of devices, causing critical bottlenecks. In this work, we propose a novel doubly communication-efficient zero-order (ZO) method with a one-point gradient estimator that replaces communicating long vectors with scalar values and that harnesses the nature of the wireless communication channel, overcoming the need to know the channel state coefficient. It is the first method that includes the wireless channel in the learning algorithm itself instead of wasting resources to analyze it and remove its impact. We then offer a thorough analysis of the proposed zero-order federated learning (ZOFL) framework and prove that our method converges textitalmost surely, which is a novel result in nonconvex ZO optimization. We further prove a convergence rate of O(frac1√[3]K) in the nonconvex setting. We finally demonstrate the potential of our algorithm with experimental results.