# Exploring New Frontiers in Vertical Federated Learning: the Role of Saddle Point Reformulation

arXiv: https://arxiv.org/abs/2602.15996 · HTML: https://mlsanity.com/paper/2602.15996/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 70 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 30 of 36)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [Error Feedback Fixes SignSGD and other Gradient Compression Schemes](https://mlsanity.com/paper/1901.09847/) (2019)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [PowerSGD: Practical Low-Rank Gradient Compression for Distributed Optimization](https://mlsanity.com/paper/1905.13727/) (2019)
- [Client Selection in Federated Learning: Convergence Analysis and Power-of-Choice Selection Strategies](https://mlsanity.com/paper/2010.01243/) (2020)
- [A Survey on Distributed Machine Learning](https://mlsanity.com/paper/1912.09789/) (2019)
- [Minimizing Finite Sums with the Stochastic Average Gradient](https://mlsanity.com/paper/1309.2388/) (2013)
- [A Survey on Homomorphic Encryption Schemes: Theory and Implementation](https://mlsanity.com/paper/1704.03578/) (2017)
- [On Biased Compression for Distributed Learning](https://mlsanity.com/paper/2002.12410/) (2020)
- [EF21: A New, Simpler, Theoretically Better, and Practically Faster Error Feedback](https://mlsanity.com/paper/2106.05203/) (2021)
- [Optimal Client Sampling for Federated Learning](https://mlsanity.com/paper/2010.13723/) (2020)
- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [Natural Compression for Distributed Deep Learning](https://mlsanity.com/paper/1905.10988/) (2019)
- [CoCoA: A General Framework for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1611.02189/) (2016)
- [Vertical Federated Learning: Challenges, Methodologies and Experiments](https://mlsanity.com/paper/2202.04309/) (2022)
- [Stochastic Variance Reduction for Variational Inequality Methods](https://mlsanity.com/paper/2102.08352/) (2021)
- [Error Compensated Distributed SGD Can Be Accelerated](https://mlsanity.com/paper/2010.00091/) (2020)
- [Communication-Efficient Federated Learning via Optimal Client Sampling](https://mlsanity.com/paper/2007.15197/) (2020)
- [When Homomorphic Encryption Marries Secret Sharing: Secure Large-Scale Sparse Logistic Regression and Applications in Risk Control](https://mlsanity.com/paper/2008.08753/) (2020)
- [A Survey on Vertical Federated Learning: From a Layered Perspective](https://mlsanity.com/paper/2304.01829/) (2023)
- [On Lower Iteration Complexity Bounds for the Saddle Point Problems](https://mlsanity.com/paper/1912.07481/) (2019)
- [Vertical Federated Learning: A Structured Literature Review](https://mlsanity.com/paper/2212.00622/) (2022)
- [On Optimal Probabilities in Stochastic Coordinate Descent Methods](https://mlsanity.com/paper/1310.3438/) (2013)
- [Coordinate Descent with Arbitrary Sampling I: Algorithms and Complexity](https://mlsanity.com/paper/1412.8060/) (2014)
- [Learning Privately over Distributed Features: An ADMM Sharing Approach](https://mlsanity.com/paper/1907.07735/) (2019)
- [Failure Prediction in Production Line Based on Federated Learning: An Empirical Study](https://mlsanity.com/paper/2101.11715/) (2021)

## Abstract (arXiv)

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.