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Robust Optimization in Federated Learning for Industrial IoT: Mathematical Foundations

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: closed (10 January 2026) | Viewed by 2411

Special Issue Editors


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Guest Editor
School of Artificial Intelligence, Guilin University of Electronic Technology, Guilin, China
Interests: distributed artificial intelligence; robust optimization; wireless sensor network
Special Issues, Collections and Topics in MDPI journals
Faculty of Education, Southwest University, Chongqing 400715, China
Interests: intelligent E-Learning environments; virtual reality in education; AI in education
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As the Industrial Internet of Things (IIoT) continues to reshape industrial landscapes, Federated Learning (FL) has emerged as a promising paradigm for collaborative machine learning across decentralized edge devices. However, the inherent challenges of dealing with uncertainties, security threats, and privacy concerns in IIoT environments necessitate robust optimization techniques. However, we can: explore novel mathematical models that enhance the robustness of FL in the face of uncertainties; develop mathematics solutions that integrate security measures into FL process, ensuring the integrity of model updates; introduce robust optimization techniques that minimize communication overhead in IIoT environments. This Special Issue aims to explore the mathematical foundations of robust optimization in FL for the Industrial IoT, providing a platform for researchers and practitioners to address critical issues and propel the field forward.

This Special Issue aims to advance the understanding and application of robust optimization in FL for the Industrial IoT through rigorous mathematical foundations. Your contributions are vital in shaping the future of intelligent and secure IIoT systems.

We invite contributions on, but not limited to, the following topics:

  • Advanced mathematical models for robust optimization in Federated Learning;
  • Innovative algorithms addressing uncertainties and dynamic conditions in the Industrial IoT;
  • Privacy-preserving algorithms for secure collaboration in IIoT environments;
  • Ensuring the integrity and authenticity of model updates in IIoT scenarios;
  • Approaches for handling device heterogeneity in Federated Learning;
  • Models and algorithms adapting to the dynamic nature of IIoT ecosystems;
  • Applications of robust optimization in practical IIoT scenarios;
  • Collaborative efforts between mathematicians, computer scientists, and industrial experts;
  • Interdisciplinary research contributing to the advancement of FL in the Industrial IoT.

Dr. Chunjiong Zhang
Dr. Tao Xie
Guest Editors

Manuscript Submission Information

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Keywords

  • robust optimization
  • Federated Learning (FL)
  • Industrial Internet of Things (IIoT)
  • mathematical foundations
  • communication-efficient optimization
  • privacy-preserving techniques
  • cybersecurity
  • IIoT edge devices
  • data privacy

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Published Papers (1 paper)

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Research

20 pages, 1672 KB  
Article
Robust Stochastic Power Allocation for Industrial IoT Federated Learning with Neurosymbolic AI
by Pratik Goswami, Adeel Iqbal and Kwonhue Choi
Mathematics 2026, 14(3), 547; https://doi.org/10.3390/math14030547 - 3 Feb 2026
Viewed by 455
Abstract
In this work, a robust optimization approach for energy-aware federated learning (FL) in industrial IoT networks is proposed that addresses uncertainties in harvested energy, device failures, and dynamic topologies. The proposed neurosymbolic reasoning approach combines graph neural networks (GNNs) for topology-aware power prediction [...] Read more.
In this work, a robust optimization approach for energy-aware federated learning (FL) in industrial IoT networks is proposed that addresses uncertainties in harvested energy, device failures, and dynamic topologies. The proposed neurosymbolic reasoning approach combines graph neural networks (GNNs) for topology-aware power prediction with symbolic rules to solve the stochastic power allocation problem, providing both optimality guarantees and explainable safety-critical decisions. The hierarchical Master-Coordination-Task Agent (MA-CoA-TA) architecture prioritizes critical industrial nodes while ensuring FL convergence under energy constraints. This work establishes approximation guarantees through theoretical analysis relative to the robust optimum and validates with rigorous simulations against existing methods. Experimental results demonstrate that proposed framework provides optimal balance for robust FL deployment in large-scale IIoT networks with real-world uncertainties by achieving 5.7% FL accuracy with 151 J remaining battery under the most challenging conditions (100 rounds, 200 devices), while baselines fail completely (0% accuracy, battery depletion). Ablation confirms component synergy—symbolic reasoning delivers 2.2 times accuracy over GNN-only, while GNN+harvesting preserves 30 times more battery than symbolic-only. Full article
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