# Byzantine-Resilient Decentralized Stochastic Optimization with Robust Aggregation Rules

arXiv: https://arxiv.org/abs/2206.04568 · HTML: https://mlsanity.com/paper/2206.04568/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2022.

## Built on by (most cited first, 23 of 23)

- [Byzantine-Robust Distributed Online Learning: Taming Adversarial Participants in An Adversarial Environment](https://mlsanity.com/paper/2307.07980/) (2023)
- [On the Tradeoff between Privacy Preservation and Byzantine-Robustness in Decentralized Learning](https://mlsanity.com/paper/2308.14606/) (2023)
- [Unified Breakdown Analysis for Byzantine Robust Gossip](https://mlsanity.com/paper/2410.10418/) (2024)
- [Generalization Error Matters in Decentralized Learning Under Byzantine Attacks](https://mlsanity.com/paper/2407.08632/) (2024)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Decentralized Adversarial Training over Graphs](https://mlsanity.com/paper/2303.13326/) (2023)
- [Byzantine-Resilient Decentralized Multi-Armed Bandits](https://mlsanity.com/paper/2310.07320/) (2023)
- [Review of Mathematical Optimization in Federated Learning](https://mlsanity.com/paper/2412.01630/) (2024)
- [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)
- [Attacks on Robust Distributed Learning Schemes via Sensitivity Curve Maximization](https://mlsanity.com/paper/2304.14024/) (2023)
- [Byzantine-Robust Gossip: Insights from a Dual Approach](https://mlsanity.com/paper/2405.03449/) (2024)
- [Generalization Error Analysis for Attack-Free and Byzantine-Resilient Decentralized Learning with Data Heterogeneity](https://mlsanity.com/paper/2506.09438/) (2025)
- [Data Quality in Edge Machine Learning: A State-of-the-Art Survey](https://mlsanity.com/paper/2406.02600/) (2024)
- [GRANITE : a Byzantine-Resilient Dynamic Gossip Learning Framework](https://mlsanity.com/paper/2504.17471/) (2025)
- [Coded Robust Aggregation for Distributed Learning under Byzantine Attacks](https://mlsanity.com/paper/2506.01989/) (2025)
- [ImprovDML: Improved Trade-off in Private Byzantine-Resilient Distributed Machine Learning](https://mlsanity.com/paper/2506.15181/) (2025)
- [Adaptive Decentralized Federated Learning for Robust Optimization](https://mlsanity.com/paper/2512.02852/) (2025)
- [DFedReweighting: A Unified Framework for Objective-Oriented Reweighting in Decentralized Federated Learning](https://mlsanity.com/paper/2512.12022/) (2025)
- [Topology-Independent Robustness of the Weighted Mean under Label Poisoning Attacks in Heterogeneous Decentralized Learning](https://mlsanity.com/paper/2601.02682/) (2026)
- [Convergence of Byzantine-Resilient Gradient Tracking via Probabilistic Edge Dropout](https://mlsanity.com/paper/2604.00449/) (2026)
- [Byzantine Accountability Without Consensus: Strong Eventual Consistency for Non-Associative, Stochastic, Robust Aggregation](https://mlsanity.com/paper/2607.10305/) (2026)
- [Fully Byzantine-Resilient Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2609.25701/) (2026)

## Abstract (arXiv)

This paper focuses on decentralized stochastic optimization in the presence of Byzantine attacks. During the optimization process, an unknown number of malfunctioning or malicious workers, termed as Byzantine workers, disobey the algorithmic protocol and send arbitrarily wrong messages to their neighbors. Even though various Byzantine-resilient algorithms have been developed for distributed stochastic optimization with a central server, we show that there are two major issues in the existing robust aggregation rules when being applied to the decentralized scenario: disagreement and non-doubly stochastic virtual mixing matrix. This paper provides comprehensive analysis that discloses the negative effects of these two issues, and gives guidelines of designing favorable Byzantine-resilient decentralized stochastic optimization algorithms. Under these guidelines, we propose iterative outlier scissor (IOS), an iterative filtering-based robust aggregation rule with provable performance guarantees. Numerical experiments demonstrate the effectiveness of IOS. The code of simulation implementation is available at github.com/Zhaoxian-Wu/IOS.