Exploring New Frontiers in Vertical Federated Learning: the Role of Saddle Point Reformulation
Beznosikov, Aleksandr Kormakov, Georgiy Grigorievskiy, Alexander Rudakov, Mikhail Nazykov, Ruslan Rogozin, Alexander Vakhrushev, Anton Savchenko, Andrey Takac, Martin Gasnikov, Alexander
Beznosikov, Aleksandr
Kormakov, Georgiy
Grigorievskiy, Alexander
Rudakov, Mikhail
Nazykov, Ruslan
Rogozin, Alexander
Vakhrushev, Anton
Savchenko, Andrey
Takac, Martin
Gasnikov, Alexander
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Machine Learning
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Journal article
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English
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Abstract
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.
Citation
A. Beznosikov, G. Kormakov, A. Grigorievskiy, M. Rudakov, R. Nazykov, A. Rogozin , et al., "Exploring New Frontiers in Vertical Federated Learning: the Role of Saddle Point Reformulation," Journal of Optimization Theory and Applications, vol. 209, no. 1, pp. 18-18, 2026, https://doi.org/10.1007/s10957-026-02961-z.
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Journal of Optimization Theory and Applications
Conference
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49 Mathematical Sciences, 4901 Applied Mathematics
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Springer Nature