# ByRDiE: Byzantine-resilient distributed coordinate descent for decentralized learning

arXiv: https://arxiv.org/abs/1708.08155 · HTML: https://mlsanity.com/paper/1708.08155/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2017.

## Built on by (most cited first, 30 of 36)

- [Decentralized Federated Learning: Balancing Communication and Computing Costs](https://mlsanity.com/paper/2107.12048/) (2021)
- [Byzantine-Robust Decentralized Learning via ClippedGossip](https://mlsanity.com/paper/2202.01545/) (2022)
- [BROADCAST: Reducing Both Stochastic and Compression Noise to Robustify Communication-Efficient Federated Learning](https://mlsanity.com/paper/2104.06685/) (2021)
- [Secure Distributed Training at Scale](https://mlsanity.com/paper/2106.11257/) (2021)
- [Robust Collaborative Learning with Linear Gradient Overhead](https://mlsanity.com/paper/2209.10931/) (2022)
- [Backdoor Attacks in Peer-to-Peer Federated Learning](https://mlsanity.com/paper/2301.09732/) (2023)
- [On the Tradeoff between Privacy Preservation and Byzantine-Robustness in Decentralized Learning](https://mlsanity.com/paper/2308.14606/) (2023)
- [Byzantine Fault-Tolerance in Federated Local SGD under 2f-Redundancy](https://mlsanity.com/paper/2108.11769/) (2021)
- [Robust Distributed Optimization With Randomly Corrupted Gradients](https://mlsanity.com/paper/2106.14956/) (2021)
- [MixTailor: Mixed Gradient Aggregation for Robust Learning Against Tailored Attacks](https://mlsanity.com/paper/2207.07941/) (2022)
- [Bristle: Decentralized Federated Learning in Byzantine, Non-i.i.d. Environments](https://mlsanity.com/paper/2110.11006/) (2021)
- [Privacy-Preserving Aggregation for Decentralized Learning with Byzantine-Robustness](https://mlsanity.com/paper/2404.17970/) (2024)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Byzantine-Resilient Decentralized Multi-Armed Bandits](https://mlsanity.com/paper/2310.07320/) (2023)
- [Resilience in Online Federated Learning: Mitigating Model-Poisoning Attacks via Partial Sharing](https://mlsanity.com/paper/2403.13108/) (2024)
- [The poison of dimensionality](https://mlsanity.com/paper/2409.17328/) (2024)
- [Review of Mathematical Optimization in Federated Learning](https://mlsanity.com/paper/2412.01630/) (2024)
- [Variance Reduction is an Antidote to Byzantines: Better Rates, Weaker Assumptions and Communication Compression as a Cherry on the Top](https://mlsanity.com/paper/2206.00529/) (2022)
- [Byzantine-Robust Decentralized Stochastic Optimization with Stochastic Gradient Noise-Independent Learning Error](https://mlsanity.com/paper/2308.05292/) (2023)
- [Competitive Advantage Attacks to Decentralized Federated Learning](https://mlsanity.com/paper/2310.13862/) (2023)
- [Stochastic Alternating Direction Method of Multipliers for Byzantine-Robust Distributed Learning](https://mlsanity.com/paper/2106.06891/) (2021)
- [Attacks on Robust Distributed Learning Schemes via Sensitivity Curve Maximization](https://mlsanity.com/paper/2304.14024/) (2023)
- [Mitigating Data Injection Attacks on Federated Learning](https://mlsanity.com/paper/2312.02102/) (2023)
- [On the Conflict of Robustness and Learning in Collaborative Machine Learning](https://mlsanity.com/paper/2402.13700/) (2024)
- [Design and Analysis of Robust Resilient Diffusion over Multi-Task Networks Against Byzantine Attacks](https://mlsanity.com/paper/2206.12749/) (2022)
- [Randomized Kaczmarz in Adversarial Distributed Setting](https://mlsanity.com/paper/2302.14615/) (2023)
- [Byzantine-Resilient Learning Beyond Gradients: Distributing Evolutionary Search](https://mlsanity.com/paper/2304.13540/) (2023)
- [VALID: a Validated Algorithm for Learning in Decentralized Networks with Possible Adversarial Presence](https://mlsanity.com/paper/2405.07316/) (2024)
- [Resilient Peer-to-peer Learning based on Adaptive Aggregation](https://mlsanity.com/paper/2501.04610/) (2025)
- [GRANITE : a Byzantine-Resilient Dynamic Gossip Learning Framework](https://mlsanity.com/paper/2504.17471/) (2025)

## Abstract (arXiv)

Distributed machine learning algorithms enable learning of models from datasets that are distributed over a network without gathering the data at a centralized location. While efficient distributed algorithms have been developed under the assumption of faultless networks, failures that can render these algorithms nonfunctional occur frequently in the real world. This paper focuses on the problem of Byzantine failures, which are the hardest to safeguard against in distributed algorithms. While Byzantine fault tolerance has a rich history, existing work does not translate into efficient and practical algorithms for high-dimensional learning in fully distributed (also known as decentralized) settings. In this paper, an algorithm termed Byzantine-resilient distributed coordinate descent (ByRDiE) is developed and analyzed that enables distributed learning in the presence of Byzantine failures. Theoretical analysis (convex settings) and numerical experiments (convex and nonconvex settings) highlight its usefulness for high-dimensional distributed learning in the presence of Byzantine failures.