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 learning performance of the global model owned by the model owner (i.e., the cloud server). However, strategies to motivate clients with high-quality contributions to join the FL training process and share trained model updates during CLPs remain underexplored. Additionally, existing incentive mechanisms in FL treat all training periods equally, which consequently fails to motivate clients to participate early. Compounding this challenge is the cloud's limited knowledge of client training capabilities due to privacy regulations, leading to information asymmetry. Therefore, in this article, we propose a time-aware incentive mechanism, called Right Reward Right Time (R3T), to encourage client involvement, especially during CLPs, to maximize the utility of the cloud in FL. Specifically, the cloud utility function captures the trade-off between the achieved model performance and payments allocated for clients' contributions, while accounting for clients' time and system capabilities, efforts, joining time, and rewards. Then, we analytically derive the optimal contract for the cloud and devise a CLP-aware mechanism to incentivize early participation and efforts while maximizing cloud utility, even under information asymmetry. 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 increases cloud utility and is more economically effective than benchmarks. Notably, our proof-of-concept results show up to a 47.6% reduction in the total number of clients and up to a 300% improvement in convergence time while reaching competitive test accuracies compared with incentive mechanism benchmarks.

Given the revolutionary role of metaverses, healthcare metaverses are emerging as a transformative force, creating intelligent healthcare systems that offer immersive and personalized services. The healthcare metaverses allow for effective decision-making and data analytics for users. However, there still exist critical challenges in building healthcare metaverses, such as the risk of sensitive data leakage and issues with sensing data security and freshness, as well as concerns around incentivizing data sharing. In this paper, we first design a user-centric privacy-preserving framework based on decentralized Federated Learning (FL) for healthcare metaverses. To further improve the privacy protection of healthcare metaverses, a cross-chain empowered FL framework is utilized to enhance sensing data security. This framework utilizes a hierarchical cross-chain architecture with a main chain and multiple subchains to perform decentralized, privacy-preserving, and secure data training in both virtual and physical spaces. Moreover, we utilize Age of Information (AoI) as an effective data-freshness metric and propose an AoI-based contract theory model under Prospect Theory (PT) to motivate sensing data sharing in a user-centric manner. This model exploits PT to better capture the subjective utility of the service provider. Finally, our numerical results demonstrate the effectiveness of the proposed schemes for healthcare metaverses.