# Distributed Interference-Aware Power Optimization for Multi-Task Over-the-Air Federated Learning
## 5 Numerical Results
### Multi-Task Ridge Regression Performance
The Pareto boundary is delineated by varying the profile vector of the centralized power control scheme as \(\kappa=[\kappa_{m},1-\kappa_{m}]\), where \(\kappa_{m}=[0.001,0.01,0.1,0.3,0.4,0.5,0.6,0.7,0.9,0.99,0.999]\). The bottom-leftmost point on the Pareto boundary by the centralized scheme represents the Pareto-optimal point, while the bottom-leftmost point by the benchmark without AirComp denotes the idealized learning performance, which serves as a benchmark for evaluating the proximity of practical schemes to optimal performance. It is observed that the Pareto-optimal point lies closest to this idealized benchmark, indicating that the centralized scheme achieves the best practical performance. Furthermore, the proposed distributed scheme demonstrates a performance remarkably closer to the Pareto-optimal point, with deviations within \(10^{-4}\), which demonstrates its efficacy in approaching centralized optimality. This proximity underscores its practical applicability, especially in scenarios constrained by communication resources. In contrast, the benchmark without interference exhibits inferior overall performance, which highlights the importance of considering inter-cell dynamics. The benchmark with maximum power performs the worst due to a lack of power adjustment or interference management. Figure 5 demonstrates the convergence behavior of the proposed distributed scheme by depicting the evolution of the optimality gap for Cell 1 and Cell 2 across iterative rounds with \(K=10\) and \(K=20\) devices per cell. The results demonstrate that all schemes converge within 30 rounds. (While our scheme demonstrates convergence within approximately  
Figure 4: Achievable optimality gap region. Figure 3: Learning performance on synthetic datasets versus communication rounds. 30 global rounds, we do not compare directly with FedAvg or FedProx, as these methods operate under fundamentally different assumptions. As such, we evaluate against baselines that are aligned with our system model to ensure a fair and meaningful comparison.) Comparative analysis between the two device configurations reveals that, under the same number of iterations, the scenario with \(K=20\) devices per cell attains a significantly lower optimality gap than the \(K=10\) scenario. This suggests that incorporating more devices into the optimization process enhances the overall system performance, which drives the learning outcomes closer to the optimal solution. Such scalability is crucial for practical applications, where the number of participating devices can vary. While an increased number of devices introduces greater complexity in collaborative computation and power adjustment, potentially leading to a slight reduction in convergence speed, the algorithm maintains stable convergence within a limited number of iterations. This resilience confirms the effectiveness of the proposed distributed scheme in managing complex multi-cell scenarios, thereby ensuring reliable performance even as the network scales.