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 further investigate whether allowing federated unlearning is beneficial to the server and users, compared to a scenario without unlearning. Interestingly, users usually have a larger total payoff in the scenario with higher costs, due to the server's excess incentives under information asymmetry. 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被遗忘的权利，联邦反学习旨在消除离群用户数据对全局学习模型的影响。当前联邦反学习的研究主要集中于开发有效且高效的反学习技术。然而，如何激励高价值用户保持参与并防止其数据被反学习的问题仍未得到充分探索，但这对反学习模型的性能至关重要。本文聚焦激励问题，为联邦学习及反学习设计了一种激励机制。我们首先刻画离群用户对全局模型精度及反学习所需通信轮次的影响。基于这些结果，我们提出一个四阶段博弈模型以捕捉学习与反学习过程中的交互与信息更新。关键贡献在于将用户的多维私有信息汇总为一维指标以指导激励设计。我们进一步探究允许联邦反学习相较于无反学习场景对服务器与用户是否更有利。有趣的是，在高成本场景下用户通常获得更大总收益，这是由于信息不对称下服务器提供的超额激励。数值结果证明了反学习激励对保留高价值离群用户的必要性，同时表明我们提出的机制相比最先进基准可将服务器成本降低高达53.91%。