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Fairness-Utilization Trade-off in Wireless Networks with Explainable Kolmogorov-Arnold Networks

Masoud Shokrnezhad, Hamidreza Mazandarani, Tarik Taleb

TL;DR

A novel approach utilizing Kolmogorov-Arnold Networks (KANs), a class of machine learning models that offer low inference costs compared to traditional DNNs through superior explainability is introduced, aiming to optimize $\alpha$-fairness to balance network utilization and user equity in wireless networks.

Abstract

The effective distribution of user transmit powers is essential for the significant advancements that the emergence of 6G wireless networks brings. In recent studies, Deep Neural Networks (DNNs) have been employed to address this challenge. However, these methods frequently encounter issues regarding fairness and computational inefficiency when making decisions, rendering them unsuitable for future dynamic services that depend heavily on the participation of each individual user. To address this gap, this paper focuses on the challenge of transmit power allocation in wireless networks, aiming to optimize $α$-fairness to balance network utilization and user equity. We introduce a novel approach utilizing Kolmogorov-Arnold Networks (KANs), a class of machine learning models that offer low inference costs compared to traditional DNNs through superior explainability. The study provides a comprehensive problem formulation, establishing the NP-hardness of the power allocation problem. Then, two algorithms are proposed for dataset generation and decentralized KAN training, offering a flexible framework for achieving various fairness objectives in dynamic 6G environments. Extensive numerical simulations demonstrate the effectiveness of our approach in terms of fairness and inference cost. The results underscore the potential of KANs to overcome the limitations of existing DNN-based methods, particularly in scenarios that demand rapid adaptation and fairness.

Fairness-Utilization Trade-off in Wireless Networks with Explainable Kolmogorov-Arnold Networks

TL;DR

A novel approach utilizing Kolmogorov-Arnold Networks (KANs), a class of machine learning models that offer low inference costs compared to traditional DNNs through superior explainability is introduced, aiming to optimize -fairness to balance network utilization and user equity in wireless networks.

Abstract

The effective distribution of user transmit powers is essential for the significant advancements that the emergence of 6G wireless networks brings. In recent studies, Deep Neural Networks (DNNs) have been employed to address this challenge. However, these methods frequently encounter issues regarding fairness and computational inefficiency when making decisions, rendering them unsuitable for future dynamic services that depend heavily on the participation of each individual user. To address this gap, this paper focuses on the challenge of transmit power allocation in wireless networks, aiming to optimize -fairness to balance network utilization and user equity. We introduce a novel approach utilizing Kolmogorov-Arnold Networks (KANs), a class of machine learning models that offer low inference costs compared to traditional DNNs through superior explainability. The study provides a comprehensive problem formulation, establishing the NP-hardness of the power allocation problem. Then, two algorithms are proposed for dataset generation and decentralized KAN training, offering a flexible framework for achieving various fairness objectives in dynamic 6G environments. Extensive numerical simulations demonstrate the effectiveness of our approach in terms of fairness and inference cost. The results underscore the potential of KANs to overcome the limitations of existing DNN-based methods, particularly in scenarios that demand rapid adaptation and fairness.

Paper Structure

This paper contains 14 sections, 7 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. System Model
  4. Problem Formulation
  5. Complexity Analysis
  6. Proposed Solution
  7. The Formulation of KANs
  8. Dataset Generation
  9. Model Training
  10. Evaluation
  11. Setup
  12. Inference Cost
  13. fairness
  14. Conclusion

Figures (4)

  • Figure 1: The system model.
  • Figure 2: The $\alpha$-fairness of data rates for a two-user network for various transmit powers. The subplots show $\alpha$-fairness for $\alpha$ values of $0.1$, $0.3$, $0.6$ and $0.9$, respectively. Assuming that there is just one base station, channel gains are set to $0.8$ for UE 1 and $0.4$ for UE 2, representing asymmetric channel conditions. $\sigma^2$ is fixed at $0.1 W$. Transmit powers for both users range from $0.1 W$ to $10 W$. The color gradient represents the magnitude of $\alpha$-fairness, with warmer colors indicating higher utility values.
  • Figure 3: The trained KAN for a network comprising four UEs and one BS and approximated functions for each element of the input vector $\mathbb{X} = \{ h_{1, b_1}, h_{2, b_1}, h_{3, b_1}, h_{4, b_1}, \alpha \}$ to compute $p_1$. It is important to note that $r^2$ is the coefficient of determination, indicating the accuracy with which the symbolic function approximates the underlying data for each element.
  • Figure 4: The prediction error (%) for the proposed KAN solution in a network with three BSs and varying numbers of UEs (3-60), shown for different $\alpha$ values (0.1, 0.5, 0.9). The solid lines represent the average of multiple simulation results, while the shaded areas encompass the individual data points from each simulation run, illustrating the range and distribution of outcomes.