用鞍点重构解决垂直联邦学习难题，支持压缩通信与异步参与。
Exploring New Frontiers in Vertical Federated Learning: the Role of Saddle Point Reformulation
- 将垂直联邦学习重构成鞍点问题，用拉格朗日方法求解。
- 提出压缩传输、部分参与、坐标选择等实用改进，收敛性有保证。
- 适合研究联邦学习系统设计或工业部署的开发者参考。
垂直联邦学习的目标是利用不同设备上的特征联合训练模型，同时共享相同用户。本文聚焦于通过经典拉格朗日函数对VFL问题进行鞍点重构。首先证明该形式可用确定性方法求解；更重要的是，探索了多种随机化改进以适应实际场景，包括采用压缩技术实现高效信息传输、支持部分参与实现异步通信、以及通过坐标选择加速本地计算。结果表明，鞍点重构在理论和实践中均具有关键作用，为原本在标准最小化框架下难以实现的扩展提供了可能。每种算法均给出了收敛性估计，验证了其有效性。此外，还研究了其他重构方式，并通过数值实验验证了所提方法的性能与有效性。
原文摘要 · Abstract (English)
The objective of Vertical Federated Learning (VFL) is to collectively train a model using features available on different devices while sharing the same users. This paper focuses on the saddle point reformulation of the VFL problem via the classical Lagrangian function. We first demonstrate how this formulation can be solved using deterministic methods. More importantly, we explore various stochastic modifications to adapt to practical scenarios, such as employing compression techniques for efficient information transmission, enabling partial participation for asynchronous communication, and utilizing coordinate selection for faster local computation. We show that the saddle point reformulation plays a key role and opens up possibilities to use mentioned extension that seem to be impossible in the standard minimization formulation. Convergence estimates are provided for each algorithm, demonstrating their effectiveness in addressing the VFL problem. Additionally, alternative reformulations are investigated, and numerical experiments are conducted to validate performance and effectiveness of the proposed approach.
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