## 2 Related Works
### Personalized Federated Learning  
Various approaches to personalized federated learning have emerged as solutions to address client heterogeneity [23; 24]. Current methods can be broadly categorized into two paradigms: global model personalization and personalized model learning [25]. The former aims to enhance the performance of a unified shared model. One intuitive strategy involves fine-tuning the global model on client-specific local datasets to generate personalized parameters [26; 27; 28]. The other is to employ a proximal regularization term to mitigate client drift, such as FedProx [29], pFedMe [30], and Ditto [31]. In contrast, FedAlign [32] tackles statistical heterogeneity from the perspective of local learning generality rather than proximal constraints. Unlike training a single global model, local personalized models are more appropriate for heterogeneous clients. One way is to establish a pre-defined trade-off between global and local models. For instance, interpolation is conducted between the two models in L2 GD [33] and LG-FedAvg [34]. In KNN-Per [35], a local model is constructed using the k-nearest neighbor method based on interpolation; however, this requires storing all the features of the samples.  
To enhance the flexibility of the personalized model on the client side, other cluster and distillation-based methods focus on the optimization of a training framework to achieve local model personalization. FedMD [36] and FedGen [37] distill knowledge from the global teacher model to the student model on the client device, thereby enabling the client to learn a more powerful personalized model. In [38], FedFTG achieves effective knowledge distillation by transferring knowledge from local models to the global model through a generator. In [39], FCCA converts private data from each client into multivariate Gaussian distributions via a global encoder and then learns the encoded latent features. Despite these advancements, personalized federated learning still faces several challenges, such as unstable training (where personalized models often lag behind global models) and high computational overhead.  
When there is an inherent difference in the data distribution, it might be more suitable to train a federated model for each homogeneous client group through clustering methods, such as Clustered Federated Learning (CFL) [40] and Privacy-Preserving Federated Adaptation (PFA) [41], but this may lead to high computational and communication overheads. [PERSON] et al. [12] proposed a representation augmentation method, FRAug, that leverages a shared embedding generator and local RTNet to convert user consensus into personalizedclient embeddings. [PERSON] et al. [42] proposed a layer-adaptive model pruning approach that utilizes non-sensitive data on the server and distributes data across edge devices to further enhance training efficiency. [PERSON] et al. [43] proposed FedMP, an online federated learning algorithm that adaptively determines different pruning ratios for heterogeneous edge nodes. These two methods both involve aggregation strategies. [PERSON] et al. [44] proposed a meta-learning algorithm to tackle personalized federated learning, while the communication cost is ignorant. The above methods all aim to achieve personalized federated learning; however, they bring a huge computational cost or/and communication overhead as well. And the dynamic balance between overhead and performance is not considered. Therefore, in this study, we propose a DualPFL method based on non-IID data, which makes it possible to reduce the communication overhead while implementing the personalized model.