The Analysis and Optimization of Volatile Clients in Over-the-Air Federated Learning

This paper investigates the implementation of Federated Learning (FL) in an over-the-air computation system with volatile clients, where each client operates under a limited energy budget and may unexpectedly drop out during local training sessions. The dropout of clients not only wastes energy but also diminishes their participation frequency, necessitating careful client selection by the server in each communication round. However, the diversity of training tasks and the random nature of client dropout present challenges such as the absence of an explicit objective function and the unavailability of client performance metrics. To address these challenges, we first analyze the convergence of the over-the-air federated learning system with volatile clients to identify the key factor influencing the model's convergence speed. Building upon this analysis, we propose an approximation of the objective function as the optimization goal for client selection. To mitigate energy waste, we introduce a dynamic client selection strategy termed DCSE, based on Exp3 with multiple plays and energy constraints, aiming to reconcile the dilemma of unknown local training states and limited resource constraints. Theoretical analysis demonstrates that our proposed solution maintains a constant bound on the difference from the optimal solution, affirming its theoretical feasibility. Furthermore, experimental results validate the effectiveness of the proposed strategy in enhancing FL by accelerating convergence speed, improving test accuracy, and reducing wasted energy.