Comparative Metaheuristic Optimization of Federated Proximal for Regression in Heterogeneous Federated Learning Environments

Resumen

Federated Learning (FL) enables collaborative model training without sharing raw data, but its performance often degrades under heterogeneous non-identically distributed (non-IID) client data. This study evaluates population-based metaheuristic algorithms to optimize the proximal hyperparameter (μ) in the Federated Proximal (FedProx) algorithm for regression tasks under highly heterogeneous conditions. Experiments used a structured tabular dataset of 1,338 observations from an individual health insurance dataset, chosen due to its sensitive medical and demographic attributes requiring strong privacy preservation. The data were partitioned into five heterogeneous clients, with non-IID severity validated using one-way ANOVA (F = 244.9053; p = 4.6609 × 10⁻¹⁴³). Five metaheuristic methods—Differential Evolution (DE), Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Harris Hawks Optimization (HHO), and Genetic Algorithm (GA)—were compared against Grid Search and Random Search using 10-fold cross-validation. Performance was evaluated using RMSE, MAE, R², search time, and memory usage. Results show that FedProx achieved stable convergence under extreme heterogeneity, with HHO obtaining the lowest RMSE (0.7653 ± 0.0561) and PSO the highest R² (0.1468 ± 0.1793) at round 50. These findings highlight the trade-off between optimization quality and computational efficiency.