Tackling System-Induced Bias in Federated Learning: A Pricing-based Incentive Mechanism

In federated learning (FL), distributed users collaboratively train a neural network model under the coordination of a central server. However, during the training process, clients often exhibit time-varying availability and have non-independent and non-identically distributed (non-IID) datasets. This results in system-induced bias, as models trained by the available clients do not accurately represent the entire population, which includes both available and unavailable clients. To address this bias, we propose a pricing-based incentive mechanism to encourage clients to adjust their availability. First, we model the strategic interaction among a large number of FL clients as a non-cooperative game under an arbitrary pricing scheme. We demonstrate that this game is a potential game, and its equilibrium can be found by solving an optimization problem. Second, based on equilibrium analysis, we derive an optimal pricing scheme for scenarios with a large client population. For general scenarios with any number of clients, we propose a bi-level optimization algorithm that utilizes Particle Swarm Optimization (PSO) to determine the optimal pricing scheme. This algorithm can effectively handles the intricate correlation between the equilibrium and pricing scheme. Our experimental results, based on real-world client availability datasets, highlight the effectiveness of our proposed incentive mechanism in mitigating system-induced bias, with improvements of up to 99.5% compared to the uniform pricing benchmark. Furthermore, this mechanism enhances the FL convergence rate by up to 3.43 times.