# A Primal-Dual Algorithm for Hybrid Federated Learning

arXiv: https://arxiv.org/abs/2210.08106 · HTML: https://mlsanity.com/paper/2210.08106/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 14 Oct 2022.

## Builds on (most cited first, 9 of 9)

- [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)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [CoCoA: A General Framework for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1611.02189/) (2016)
- [Communication-Efficient Distributed Dual Coordinate Ascent](https://mlsanity.com/paper/1409.1458/) (2014)
- [Hybrid Federated Learning: Algorithms and Implementation](https://mlsanity.com/paper/2012.12420/) (2020)
- [Optimization for Large-Scale Machine Learning with Distributed Features and Observations](https://mlsanity.com/paper/1610.10060/) (2016)
- [A dual approach for federated learning](https://mlsanity.com/paper/2201.11183/) (2022)
- [Comprehensive Performance Analysis of Homomorphic Cryptosystems for Practical Data Processing](https://mlsanity.com/paper/2202.02960/) (2022)

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

- [Hybrid FedGraph: An efficient hybrid federated learning algorithm using graph convolutional neural network](https://mlsanity.com/paper/2404.09443/) (2024)
- [Federated Automated Feature Engineering](https://mlsanity.com/paper/2412.04404/) (2024)
- [A Hybrid Federated Kernel Regularized Least Squares Algorithm](https://mlsanity.com/paper/2407.17228/) (2024)
- [Unveiling Hidden Threats: Using Fractal Triggers to Boost Stealthiness of Distributed Backdoor Attacks in Federated Learning](https://mlsanity.com/paper/2511.09252/) (2025)

## Abstract (arXiv)

Very few methods for hybrid federated learning, where clients only hold subsets of both features and samples, exist. Yet, this scenario is extremely important in practical settings. We provide a fast, robust algorithm for hybrid federated learning that hinges on Fenchel Duality. We prove the convergence of the algorithm to the same solution as if the model is trained centrally in a variety of practical regimes. Furthermore, we provide experimental results that demonstrate the performance improvements of the algorithm over a commonly used method in federated learning, FedAvg, and an existing hybrid FL algorithm, HyFEM. We also provide privacy considerations and necessary steps to protect client data.