Exploring New Frontiers in Vertical Federated Learning: the Role of Saddle Point Reformulation
Keywords: convex optimization, saddle point problem, vertical federated learning
Abstract: Distributed learning problems have gained significant popularity due to the increasing need for cluster training and the emergence of novel paradigms like Federated Learning (FL). One variant of FL, called Vertical Federated Learning (VFL), partitions data based on features across devices. The objective is to collectively train a model using the information available on each user's device. This paper focuses on solving the VFL problem using the saddle point reformulation via the classical Lagrangian function. We first demonstrate how this formulation can be solved using deterministic methods. But more importantly, the paper explores 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 of the VFL problem are investigated, and numerical experiments are conducted to validate the proposed methods' performance and effectiveness.
Primary Area: optimization
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Submission Number: 14169
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