To protect users' right to be forgotten in federated learning, federated unlearning aims at eliminating the impact of leaving users' data on the global learned model. The current research in federated unlearning mainly concentrated on developing effective and efficient unlearning techniques. However, the issue of incentivizing valuable users to remain engaged and preventing their data from being unlearned is still under-explored, yet important to the unlearned model performance. This paper focuses on the incentive issue and develops an incentive mechanism for federated learning and unlearning. We first characterize the leaving users' impact on the global model accuracy and the required communication rounds for unlearning. Building on these results, we propose a four-stage game to capture the interaction and information updates during the learning and unlearning process. A key contribution is to summarize users' multi-dimensional private information into one-dimensional metrics to guide the incentive design. We show that users who incur high costs and experience significant training losses are more likely to discontinue their engagement through federated unlearning. The server tends to retain users who make substantial contributions to the model but has a trade-off on users' training losses, as large training losses of retained users increase privacy costs but decrease unlearning costs. The numerical results demonstrate the necessity of unlearning incentives for retaining valuable leaving users, and also show that our proposed mechanisms decrease the server's cost by up to 53.91% compared to state-of-the-art benchmarks.

翻译：为保护联邦学习中用户的被遗忘权，联邦遗忘学习旨在消除离群用户数据对全局已训练模型的影响。当前联邦遗忘学习的研究主要集中在开发高效且有效的遗忘技术。然而，如何激励有价值的用户保持参与并防止其数据被遗忘这一问题仍待深入探讨，且对遗忘后模型性能具有重要影响。本文聚焦激励机制问题，提出了一种面向联邦学习与遗忘学习的激励框架。我们首先量化了离群用户对全局模型精度的影响以及执行遗忘所需通信轮次。基于上述结果，提出了四阶段博弈模型以捕捉学习与遗忘过程中的交互行为与信息更新。核心贡献在于将用户的多维私有信息归纳为单维指标以指导激励设计。研究表明：承担高成本且遭受显著训练损失的用户更倾向通过联邦遗忘终止参与；服务器倾向于保留对模型贡献较大的用户，但在用户训练损失上存在权衡——保留用户的训练损失增加会提升隐私成本但同时降低遗忘成本。数值结果验证了遗忘激励对保留高价值离群用户的必要性，同时表明与当前最优基准相比，所提机制可使服务器成本降低最高达53.91%。