An Incentive Mechanism for Federated Learning With Time-Varying Client Availability

In federated learning (FL), distributed users collaboratively train a neural network model under the coordination of a central server. However, time-varying client availability, coupled with non-independent and non-identically distributed (non-IID) datasets, leads to a biased convergence. In this work, we prove the convergence of FL under time-varying client availability. The theoretical result shows that biased convergence occurs when available client distribution does not algin with the client population distribution. To address this challenge, we propose a pricing-based incentive mechanism to encourage clients to adjust their availability. First, we model the strategic interactions among clients as a non-cooperative game under an arbitrary pricing scheme. We prove that this game is a potential game and its equilibrium can be found through optimization. Second, we derive an optimal pricing scheme for large client populations and propose a bi-level optimization algorithm using Particle Swarm Optimization (PSO) for general scenarios. Through analysis of client availability evolution, we prove the effectiveness of our scheme in mitigating biased convergence. Experimental results using real-world client availability dataset show that our approach addresses time-varying client availability issue, achieving up to 99.5% improvement over benchmarks and enhancing FL convergence rates by up to 2.49 times.