Critical learning periods (CLPs) in federated learning (FL) refer to early stages during which low-quality contributions (e.g., sparse training data availability) can permanently impair the performance of the global model owned by the cloud server. However, existing incentive mechanisms typically assume temporal homogeneity, treating all training rounds as equally important, thereby failing to prioritize and attract high-quality contributions during CLPs. This inefficiency is compounded by information asymmetry due to privacy regulations, where the cloud lacks knowledge of client training capabilities, leading to adverse selection and moral hazard. Thus, in this article, we propose a time-aware contract-theoretic incentive framework, named Right Reward Right Time (R3T), to encourage client involvement, especially during CLPs, to maximize the utility of the cloud server. We formulate a cloud utility function that captures the trade-off between the achieved model performance and rewards allocated for clients' contributions, explicitly accounting for client heterogeneity in time and system capabilities, effort, and joining time. Then, we devise a CLP-aware incentive mechanism deriving an optimal contract design that satisfies individual rationality, incentive compatibility, and budget feasibility constraints, motivating rational clients to participate early and contribute efforts. By providing the right reward at the right time, our approach can attract the highest-quality contributions during CLPs. Simulation and proof-of-concept studies show that R3T mitigates information asymmetry, increases cloud utility, and yields superior economic efficiency compared to conventional incentive mechanisms. Our proof-of-concept results demonstrate up to a 47.6% reduction in the total number of clients and up to a 300% improvement in convergence time while achieving competitive test accuracy.

翻译：联邦学习中的关键学习期是指早期阶段，在此期间低质量贡献（如稀疏训练数据可用性）可能永久损害云服务器所拥有的全局模型性能。然而，现有激励机制通常假设时间同质性，将所有训练轮次视为同等重要，从而无法在关键学习期优先吸引高质量贡献。由于隐私法规导致的信息不对称加剧了这种低效性，云服务器缺乏对客户端训练能力的了解，从而引发逆向选择和道德风险。因此，本文提出一种时间感知的契约理论激励框架，称为“适时适奖”，以鼓励客户端参与，特别是在关键学习期，从而最大化云服务器效用。我们构建了一个云效用函数，该函数捕捉了所达模型性能与为客户端贡献分配奖励之间的权衡，并明确考虑了客户端在时间与系统能力、努力程度和加入时间上的异质性。随后，我们设计了一种关键学习期感知激励机制，推导出满足个体理性、激励相容和预算可行性约束的最优契约设计，激励理性客户端尽早参与并付出努力。通过在正确时间提供适当奖励，我们的方法能够在关键学习期吸引最高质量的贡献。仿真与概念验证研究表明，与传统激励机制相比，R3T能够缓解信息不对称、提升云服务器效用，并产生更优的经济效率。我们的概念验证结果表明，在实现具有竞争力的测试准确率的同时，客户端总数最多可减少47.6%，收敛时间最多可提升300%。