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Federated Learning Based Analysis of Certain Complex Multivariate Functions Given by Sample Only

Nevena Mijajlović^1,2, Ajlan Zajmović², Miodrag J. Mihaljević^1,3, Wei Shao¹, Lianhai Wang¹, Shujiang Xu¹

1. Key Laboratory of Computing Power Network and Information Security, Ministry of Education,
   Shandong Computer Science Center, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China
   nevenami@ucg.ac.me
2. Faculty of Science and Mathematics, University of Montenegro, Podgorica, Montenegro
3. Serbian Academy of Sciences and Arts, Belgrade, Serbia

Abstract

We consider the problem of optimizing a complex function f(·) given a sample consisting of M input-output pairs (argument, function value), S = {(x_n, y_n)}_n=1^M, where x ∈ R^d and y ∈ R. We assume that the sample is available only in a distributed manner at K entities, where each entity controls a sample part S_k and S = ∪_k=1^KS_k. The problem is addressed employing a machine learning approach. Our goal is to generate a surrogate of the function based on the given sample, and to perform the optimization on the surrogate function. Due to the distributed nature of the sample we employ Federated Machine Learning (FML) to generate the surrogate function by joint efforts of all K entities that possess the sample parts. We call the entities involved in FML clients, and we assume that certain clients participate in FML in a malicious manner by poisoning training data or the model parameters they generate locally. Systematic experiments have been performed to study the characteristics of the surrogate function and its capabilities to provide reliable analysis of the original function depending on the sample available for training, and impacts of the training data poisoning, as well as locally generated model parameters.

Key words

Surrogate Functions, Neural Networks, Federated Machine Learning, Algorithms, Optimization Models and Methods, Minimum Evaluation, Systematic Numerical Evaluation

Digital Object Identifier (DOI)

https://doi.org/10.2298/CSIS251215035M

Publication information

Volume 23, Issue 4 (September 2026)
Year of Publication: 2026
ISSN: 2406-1018 (Online)
Publisher: ComSIS Consortium

Full text

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How to cite

Mijajlović, N., Zajmović, A., Mihaljević, M.J., Shao, W., Wang, L., Xu, S.: Federated Learning Based Analysis of Certain Complex Multivariate Functions Given by Sample Only. Computer Science and Information Systems, 23(4) (2026). https://doi.org/10.2298/CSIS251215035M