## 2 Related Work
### Accelerating Convergence in Federated Learning  
In FL, the downloading of the global model and the uploading of updated data introduce an additional communication overhead [26]. Consequently, accelerating convergence to mitigate this overhead has become a significant challenge. Various techniques have been proposed to address this [27; 28], including selective client sampling, client clustering, upload dropout and network topology optimization. FLOB [8] evaluates the contributions of clients to the global model using local update information, and determines the optimal probability distribution for client selection to confirm a near-optimal subset of clients that minimizes global loss. The Eiffel [29] algorithm dynamically selects clients for global model aggregation and adjusts the frequency of local and global model updates adaptively, which enables the server to schedule clients considering resource efficiency and model fairness. OCEAN [5] considers clients' computation and communication resource status, and selects a subset for FL uploads based on both current resource availability and historical energy state tracking. FedMCCS [30] is a multi-criterion method for selecting FL clients. It evaluates CPU, memory, energy and time resources to predict client capacity and maximize participation in FL. The limitation of these FL methods with selective client sampling is that they overlook the training requirements of clients with limited resources in the system. In FRSs that require non-global training of sub-models (i.e., client models), such negligence can slow down the training process of these clients, thus impairing the convergence speed of the entire system. [PERSON] et al. [9] introduce a cluster aggregation approach in FL, where clients synchronously transmit their local updates to cluster headers and the headers then asynchronously conduct global aggregation. They propose a cluster-based FL to optimize the cluster structure under resource constraints and apply it to dynamic networks. FedCor [10] addresses inter-client correlation using Gaussian processes to model loss correlations. By selectively sampling clients, it aims to reduce global loss per round and accelerate model convergence. These client clustering methods have only been validated on relatively small-scale models. In FRSs, as the number of items in the system increases, so does the number of item models uploaded by each client. Moreover, due to the variations in users' item interaction histories, the types of item models they upload vary significantly. Conversely, in the studies of [9; 10], the data uploaded by each client have the same dimension. These issues pose challenges to the application of client clustering methods in FRSs. [PERSON] et al. [31] propose an asynchronous model update approach, contending that general features are learned in the shallower layers of neural networks and, consequently, exert a greater influence on convergence. This method mitigates the frequency of uploading parameters from deeper layers to the server and incorporates a time-weighted aggregation strategy on the server. FedKD [32] reduces communicated parameter size via knowledge distillation. It trains a large teacher and a small student model locally. Only the student model is sent to the server. Aggregated gradients are sent back, and knowledge is transferred from student to teacher. However, in FRSs, the relatively small model size and the large number of equally important item models suggest that these dropout methods may not be applicable. [PERSON] et al. [33] introduce a ring-based decentralized FL framework for deep generative models, utilizing a unique ring topology and map-reduce synchronization to enhance efficiency and bandwidth utilization. [PERSON] et al. [6] propose a novel topology design optimizing a minimal cycle time for higher throughput in cross-silo scenarios with high-speed links. The methods proposed in [6; 33] are applicable to deep generative models and cross-silo settings, respectively.