# Optimizing Server Placement for Vertical Federated Learning in Dynamic Edge/Fog Networks

arXiv: https://arxiv.org/abs/2605.09813 · HTML: https://mlsanity.com/paper/2605.09813/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 80 references that are in the map.
- First posted on arXiv 10 May 2026.

## Builds on (most cited first, 30 of 35)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Adaptive Federated Learning in Resource Constrained Edge Computing Systems](https://mlsanity.com/paper/1804.05271/) (2018)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Implicit regularization for deep neural networks driven by an Ornstein-Uhlenbeck like process](https://mlsanity.com/paper/1904.09080/) (2019)
- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [Federated Learning over Wireless Networks: Convergence Analysis and Resource Allocation](https://mlsanity.com/paper/1910.13067/) (2019)
- [VAFL: a Method of Vertical Asynchronous Federated Learning](https://mlsanity.com/paper/2007.06081/) (2020)
- [A Proximal Stochastic Gradient Method with Progressive Variance Reduction](https://mlsanity.com/paper/1403.4699/) (2014)
- [Fast Federated Learning in the Presence of Arbitrary Device Unavailability](https://mlsanity.com/paper/2106.04159/) (2021)
- [Federated Learning Meets Multi-objective Optimization](https://mlsanity.com/paper/2006.11489/) (2020)
- [Anarchic Federated Learning](https://mlsanity.com/paper/2108.09875/) (2021)
- [Stochastic Client Selection for Federated Learning with Volatile Clients](https://mlsanity.com/paper/2011.08756/) (2020)
- [6G Internet of Things: A Comprehensive Survey](https://mlsanity.com/paper/2108.04973/) (2021)
- [Loss Functions for Top-k Error: Analysis and Insights](https://mlsanity.com/paper/1512.00486/) (2015)
- [Compressed-VFL: Communication-Efficient Learning with Vertically Partitioned Data](https://mlsanity.com/paper/2206.08330/) (2022)
- [On Lipschitz Bounds of General Convolutional Neural Networks](https://mlsanity.com/paper/1808.01415/) (2018)
- [Network-Aware Optimization of Distributed Learning for Fog Computing](https://mlsanity.com/paper/2004.08488/) (2020)
- [Improving Lipschitz-Constrained Neural Networks by Learning Activation Functions](https://mlsanity.com/paper/2210.16222/) (2022)
- [UAV-assisted Online Machine Learning over Multi-Tiered Networks: A Hierarchical Nested Personalized Federated Learning Approach](https://mlsanity.com/paper/2106.15734/) (2021)
- [Flexible Vertical Federated Learning with Heterogeneous Parties](https://mlsanity.com/paper/2208.12672/) (2022)
- [LESS-VFL: Communication-Efficient Feature Selection for Vertical Federated Learning](https://mlsanity.com/paper/2305.02219/) (2023)
- [How to escape sharp minima with random perturbations](https://mlsanity.com/paper/2305.15659/) (2023)
- [A Survey of Air-to-Ground Propagation Channel Modeling for Unmanned Aerial Vehicles](https://mlsanity.com/paper/1801.01656/) (2018)
- [Communication-Efficient Multimodal Federated Learning: Joint Modality and Client Selection](https://mlsanity.com/paper/2401.16685/) (2024)
- [Disciplined Geometric Programming](https://mlsanity.com/paper/1812.04074/) (2018)
- [Towards Cooperative Federated Learning over Heterogeneous Edge/Fog Networks](https://mlsanity.com/paper/2303.08361/) (2023)
- [Cellular UAV-to-X Communications: Design and Optimization for Multi-UAV Networks](https://mlsanity.com/paper/1801.05000/) (2018)

## Abstract (arXiv)

We investigate the control and optimization of vertical federated learning (VFL), a class of distributed machine learning (ML) methods in which edge/fog devices contain separate data features, in dynamic edge/fog networks. Owing to heterogeneous data features and hardware across edge/fog networks, devices' contributions to VFL vary substantially, and, moreover, dynamic edge/fog networks can lead to the permanent exit or entry of select data features. In this setting, our proposed methodology, server controlled VFL in dynamic networks (SC-DN), first establishes the existence of a global first-order stationary point for every global round, and then leverages this result to jointly optimize ML model training and resource consumption based on four key control variables: (i) server placement, (ii) device-to-server transmit power, (iii) local device processor frequency, and (iv) local training iterations per global round. The resulting optimization formulation contains coupled variables as well as numerous forms of logarithmic constraints which we show is a mixed-integer signomial program, an NP-hard problem, and for which we develop a general solver. Finally, via experiments on both image and multi-modal datasets, we show that our methodology demonstrates superior classification/regression performance and resource consumption savings than even greedy methodologies.