# Approximate Agreement Algorithms for Byzantine Collaborative Learning

arXiv: https://arxiv.org/abs/2504.01504 · HTML: https://mlsanity.com/paper/2504.01504/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 54 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 24 of 24)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [How To Backdoor Federated Learning](https://mlsanity.com/paper/1807.00459/) (2018)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Local Model Poisoning Attacks to Byzantine-Robust Federated Learning](https://mlsanity.com/paper/1911.11815/) (2019)
- [Analyzing Federated Learning through an Adversarial Lens](https://mlsanity.com/paper/1811.12470/) (2018)
- [The Hidden Vulnerability of Distributed Learning in Byzantium](https://mlsanity.com/paper/1802.07927/) (2018)
- [Robust Aggregation for Federated Learning](https://mlsanity.com/paper/1912.13445/) (2019)
- [Federated Optimization:Distributed Optimization Beyond the Datacenter](https://mlsanity.com/paper/1511.03575/) (2015)
- [Learning from History for Byzantine Robust Optimization](https://mlsanity.com/paper/2012.10333/) (2020)
- [Differentially Private Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2111.09278/) (2021)
- [Distributed Statistical Machine Learning in Adversarial Settings: Byzantine Gradient Descent](https://mlsanity.com/paper/1705.05491/) (2017)
- [Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)](https://mlsanity.com/paper/2008.00742/) (2020)
- [Challenges and Approaches for Mitigating Byzantine Attacks in Federated Learning](https://mlsanity.com/paper/2112.14468/) (2021)
- [Distributed Robust Learning](https://mlsanity.com/paper/1409.5937/) (2014)
- [SPEED: Secure, PrivatE, and Efficient Deep learning](https://mlsanity.com/paper/2006.09475/) (2020)
- [Byzantine Vector Consensus in Complete Graphs](https://mlsanity.com/paper/1302.2543/) (2013)
- [SignSGD with Federated Defense: Harnessing Adversarial Attacks through Gradient Sign Decoding](https://mlsanity.com/paper/2402.01340/) (2024)

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

- [Practical Validity Conditions for Byzantine-Tolerant Federated Learning](https://mlsanity.com/paper/2605.15887/) (2026)

## Abstract (arXiv)

In Byzantine collaborative learning, n clients in a peer-to-peer network collectively learn a model without sharing their data by exchanging and aggregating stochastic gradient estimates. Byzantine clients can prevent others from collecting identical sets of gradient estimates. The aggregation step thus needs to be combined with an efficient (approximate) agreement subroutine to ensure convergence of the training process. In this work, we study the geometric median aggregation rule for Byzantine collaborative learning. We show that known approaches do not provide theoretical guarantees on convergence or gradient quality in the agreement subroutine. To satisfy these theoretical guarantees, we present a hyperbox algorithm for geometric median aggregation. We practically evaluate our algorithm in both centralized and decentralized settings under Byzantine attacks on non-i.i.d. data. We show that our geometric median-based approaches can tolerate sign-flip attacks better than known mean-based approaches from the literature.