Long-Term Optimal Incentives for Differential-Privacy Federated Learning: A Multi-Stage Game Approach
Differential-privacy federated learning (DP-FL) has emerged as a promising paradigm capable of mitigating the inherent threat of traditional FL architectures that are vulnerable to inferential attacks due to the frequent exchange and updating of model parameters. However, existing DP-FL frameworks often assume that the client’s perturbations remain constant throughout the FL process, while ignoring the varying influence of the client’s perturbations in distinct communication rounds on the model performance. Besides, existing DP-FL frameworks posit the FL server as a fully rational actor, thereby neglecting the bounded rationality that the FL server may exhibit in the face of risk and uncertainty. In this paper, we propose a novel long-term (i.e., throughout the FL process) privacy-preserving FL framework to address the optimal incentive design, in the presence of the bounded rationality inherent in the FL server and the dynamic influence of perturbations on model performance. Specifically, we first investigate the impact of local perturbations of the client on the model’s convergence performance in different communication rounds, elucidating the trade-off between learning performance and privacy loss. Then, to reconcile learning performance with privacy loss, we design a long-term privacy-preserving incentive scheme, where the interactions between clients and the FL server throughout the FL process are modeled as a multi-stage privacy-preserving game. Furthermore, by applying prospect theory (PT) to formulate the risk-aware behavior of the bounded rationality FL server, we employ contract theory to derive the equilibrium of the game, thereby ensuring optimality and fairness. Finally, extensive simulations illustrate that our scheme can motivate clients to provide high-quality models and improve the accuracy of the global model, compared with benchmarks.