# Flexible Vertical Federated Learning with Heterogeneous Parties

arXiv: https://arxiv.org/abs/2208.12672 · HTML: https://mlsanity.com/paper/2208.12672/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2022.

## Built on by (most cited first, 20 of 20)

- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [FedVS: Straggler-Resilient and Privacy-Preserving Vertical Federated Learning for Split Models](https://mlsanity.com/paper/2304.13407/) (2023)
- [Advances in Robust Federated Learning: A Survey with Heterogeneity Considerations](https://mlsanity.com/paper/2405.09839/) (2024)
- [Vertical Federated Learning: Taxonomies, Threats, and Prospects](https://mlsanity.com/paper/2302.01550/) (2023)
- [VFLAIR: A Research Library and Benchmark for Vertical Federated Learning](https://mlsanity.com/paper/2310.09827/) (2023)
- [Robust and IP-Protecting Vertical Federated Learning against Unexpected Quitting of Parties](https://mlsanity.com/paper/2303.18178/) (2023)
- [Online Vertical Federated Learning for Cooperative Spectrum Sensing](https://mlsanity.com/paper/2312.11363/) (2023)
- [Communication-Efficient Hybrid Federated Learning for E-health with Horizontal and Vertical Data Partitioning](https://mlsanity.com/paper/2404.10110/) (2024)
- [Communication-efficient Vertical Federated Learning via Compressed Error Feedback](https://mlsanity.com/paper/2406.14420/) (2024)
- [Secure and Fast Asynchronous Vertical Federated Learning via Cascaded Hybrid Optimization](https://mlsanity.com/paper/2306.16077/) (2023)
- [Robust Collaborative Inference with Vertically Split Data Over Dynamic Device Environments](https://mlsanity.com/paper/2312.16638/) (2023)
- [Flexible Differentially Private Vertical Federated Learning with Adaptive Feature Embeddings](https://mlsanity.com/paper/2308.02362/) (2023)
- [Task-Oriented Edge Networks: Decentralized Learning Over Wireless Fronthaul](https://mlsanity.com/paper/2312.01288/) (2023)
- [Communication-Efficient and Differentially Private Vertical Federated Learning with Zeroth-Order Optimization](https://mlsanity.com/paper/2502.20565/) (2025)
- [Integrating Identity-Based Identification against Adaptive Adversaries in Federated Learning](https://mlsanity.com/paper/2504.03077/) (2025)
- [Deep Latent Variable Model based Vertical Federated Learning with Flexible Alignment and Labeling Scenarios](https://mlsanity.com/paper/2505.11035/) (2025)
- [Multimodal Federated Learning: A Survey through the Lens of Different FL Paradigms](https://mlsanity.com/paper/2505.21792/) (2025)
- [Proto-EVFL: Enhanced Vertical Federated Learning via Dual Prototype with Extremely Unaligned Data](https://mlsanity.com/paper/2507.22488/) (2025)
- [PubSub-VFL: Towards Efficient Two-Party Split Learning in Heterogeneous Environments via Publisher/Subscriber Architecture](https://mlsanity.com/paper/2510.12494/) (2025)
- [Optimizing Server Placement for Vertical Federated Learning in Dynamic Edge/Fog Networks](https://mlsanity.com/paper/2605.09813/) (2026)

## Abstract (arXiv)

We propose Flexible Vertical Federated Learning (Flex-VFL), a distributed machine algorithm that trains a smooth, non-convex function in a distributed system with vertically partitioned data. We consider a system with several parties that wish to collaboratively learn a global function. Each party holds a local dataset; the datasets have different features but share the same sample ID space. The parties are heterogeneous in nature: the parties' operating speeds, local model architectures, and optimizers may be different from one another and, further, they may change over time. To train a global model in such a system, Flex-VFL utilizes a form of parallel block coordinate descent, where parties train a partition of the global model via stochastic coordinate descent. We provide theoretical convergence analysis for Flex-VFL and show that the convergence rate is constrained by the party speeds and local optimizer parameters. We apply this analysis and extend our algorithm to adapt party learning rates in response to changing speeds and local optimizer parameters. Finally, we compare the convergence time of Flex-VFL against synchronous and asynchronous VFL algorithms, as well as illustrate the effectiveness of our adaptive extension.