Federated learning (FL) is a communication-efficient collaborative learning framework that enables model training across multiple agents with private local datasets. While the benefits of FL in improving global model performance are well established, individual agents may behave strategically, balancing the learning payoff against the cost of contributing their local data. Motivated by the need for FL frameworks that successfully retain participating agents, we propose an incentive-aware federated averaging method in which, at each communication round, clients transmit both their local model parameters and their updated training dataset sizes to the server. The dataset sizes are dynamically adjusted via a Nash equilibrium (NE)-seeking update rule that captures strategic data participation. We analyze the proposed method under convex and nonconvex global objective settings and establish performance guarantees for the resulting incentive-aware FL algorithm. Furthermore, under a merely monotone game setting, we consider a welfare loss minimization framework and establish asymptotic convergence of the scheme. Numerical experiments on the MNIST and CIFAR-10 datasets demonstrate that agents achieve competitive global model performance while converging to stable data participation strategies.

翻译：联邦学习（FL）是一种通信高效的协作学习框架，支持多个拥有私有本地数据集的智能体协同训练模型。尽管FL在提升全局模型性能方面的优势已得到充分验证，但个体智能体可能采取策略性行为，需要在学习收益与贡献本地数据的成本之间进行权衡。为了满足联邦学习框架成功保留参与智能体的需求，我们提出了一种激励感知的联邦平均方法。在每个通信轮次中，客户端向服务器同时传输其本地模型参数和更新后的训练数据集规模。数据集规模通过一种纳什均衡（NE）搜索更新规则进行动态调整，该规则能够捕捉策略性数据参与行为。我们在凸性及非凸性全局目标设定下对所提方法进行分析，并为该激励感知联邦学习算法建立性能保障。此外，在仅需单调博弈设定的条件下，我们考虑了一个福利损失最小化框架，并证明了该方案的渐近收敛性。在MNIST和CIFAR-10数据集上的数值实验表明，智能体在收敛至稳定数据参与策略的同时，能够获得具有竞争力的全局模型性能。