# Byzantine-Robust and Differentially Private Federated Optimization under Weaker Assumptions

arXiv: https://arxiv.org/abs/2603.23472 · HTML: https://mlsanity.com/paper/2603.23472/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 120 references that are in the map.
- First posted on arXiv 24 Mar 2026.

## Builds on (most cited first, 30 of 41)

- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [The Hidden Vulnerability of Distributed Learning in Byzantium](https://mlsanity.com/paper/1802.07927/) (2018)
- [Byzantine-Robust Learning on Heterogeneous Datasets via Bucketing](https://mlsanity.com/paper/2006.09365/) (2020)
- [Decentralized Deep Learning with Arbitrary Communication Compression](https://mlsanity.com/paper/1907.09356/) (2019)
- [Stochastic Controlled Averaging for Federated Learning with Communication Compression](https://mlsanity.com/paper/2308.08165/) (2023)
- [On the Convergence of SGD with Biased Gradients](https://mlsanity.com/paper/2008.00051/) (2020)
- [Byzantine-Resilient Non-Convex Stochastic Gradient Descent](https://mlsanity.com/paper/2012.14368/) (2020)
- [FedNL: Making Newton-Type Methods Applicable to Federated Learning](https://mlsanity.com/paper/2106.02969/) (2021)
- [A Better Alternative to Error Feedback for Communication-Efficient Distributed Learning](https://mlsanity.com/paper/2006.11077/) (2020)
- [A Reputation Mechanism Is All You Need: Collaborative Fairness and Adversarial Robustness in Federated Learning](https://mlsanity.com/paper/2011.10464/) (2020)
- [Learning Differentially Private Recurrent Language Models](https://mlsanity.com/paper/1710.06963/) (2017)
- [Byzantine-Robust Decentralized Learning via ClippedGossip](https://mlsanity.com/paper/2202.01545/) (2022)
- [Fine-Tuning Large Language Models with User-Level Differential Privacy](https://mlsanity.com/paper/2407.07737/) (2024)
- [Mind the Privacy Unit! User-Level Differential Privacy for Language Model Fine-Tuning](https://mlsanity.com/paper/2406.14322/) (2024)
- [Differential Privacy and Byzantine Resilience in SGD: Do They Add Up?](https://mlsanity.com/paper/2102.08166/) (2021)
- [The Privacy Power of Correlated Noise in Decentralized Learning](https://mlsanity.com/paper/2405.01031/) (2024)
- [Adaptive Compression for Communication-Efficient Distributed Training](https://mlsanity.com/paper/2211.00188/) (2022)
- [Basis Matters: Better Communication-Efficient Second Order Methods for Federated Learning](https://mlsanity.com/paper/2111.01847/) (2021)
- [EControl: Fast Distributed Optimization with Compression and Error Control](https://mlsanity.com/paper/2311.05645/) (2023)
- [The Error-Feedback Framework: Better Rates for SGD with Delayed Gradients and Compressed Communication](https://mlsanity.com/paper/1909.05350/) (2019)
- [Bridging Differential Privacy and Byzantine-Robustness via Model Aggregation](https://mlsanity.com/paper/2205.00107/) (2022)
- [Clip21: Error Feedback for Gradient Clipping](https://mlsanity.com/paper/2305.18929/) (2023)
- [Compression with Exact Error Distribution for Federated Learning](https://mlsanity.com/paper/2310.20682/) (2023)
- [Adaptive Gradient Clipping for Robust Federated Learning](https://mlsanity.com/paper/2405.14432/) (2024)
- [Dynamic Defense Against Byzantine Poisoning Attacks in Federated Learning](https://mlsanity.com/paper/2007.15030/) (2020)
- [Why Do We Need Warm-up? A Theoretical Perspective](https://mlsanity.com/paper/2510.03164/) (2025)
- [Optimal Decentralized Distributed Algorithms for Stochastic Convex Optimization](https://mlsanity.com/paper/1911.07363/) (2019)
- [DoCoM: Compressed Decentralized Optimization with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2202.00255/) (2022)
- [Safe-EF: Error Feedback for Nonsmooth Constrained Optimization](https://mlsanity.com/paper/2505.06053/) (2025)
- [Towards Faster Decentralized Stochastic Optimization with Communication Compression](https://mlsanity.com/paper/2405.20114/) (2024)

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

- [Theoretical Foundations of Communication-Efficient, Robust, and Practical Distributed and Federated Optimization](https://mlsanity.com/paper/2608.06563/) (2026)

## Abstract (arXiv)

Federated Learning (FL) enables heterogeneous clients to collaboratively train a shared model without centralizing their raw data, offering an inherent level of privacy. However, gradients and model updates can still leak sensitive information, while malicious servers may mount adversarial attacks such as Byzantine manipulation. These vulnerabilities highlight the need to address differential privacy (DP) and Byzantine robustness within a unified framework. Existing approaches, however, often rely on unrealistic assumptions such as bounded gradients, require auxiliary server-side datasets, or fail to provide convergence guarantees. We address these limitations by proposing Byz-Clip21-SGD2M, a new algorithm that integrates robust aggregation with double momentum and carefully designed clipping. We prove high-probability convergence guarantees under standard L-smoothness and σ-sub-Gaussian gradient noise assumptions, thereby relaxing conditions that dominate prior work. Our analysis recovers state-of-the-art convergence rates in the absence of adversaries and improves utility guarantees under Byzantine and DP settings. Empirical evaluations on CNN and MLP models trained on MNIST further validate the effectiveness of our approach.