  Personalized federated learning (PFL) aims to produce the greatest
personalized model for each client to face an insurmountable problem--data
heterogeneity in real FL systems. However, almost all existing works have to
face large communication burdens and the risk of disruption if the central
server fails. Only limited efforts have been used in a decentralized way but
still suffers from inferior representation ability due to sharing the full
model with its neighbors. Therefore, in this paper, we propose a personalized
FL framework with a decentralized partial model training called DFedAlt. It
personalizes the "right" components in the modern deep models by alternately
updating the shared and personal parameters to train partially personalized
models in a peer-to-peer manner. To further promote the shared parameters
aggregation process, we propose DFedSalt integrating the local Sharpness Aware
Minimization (SAM) optimizer to update the shared parameters. It adds proper
perturbation in the direction of the gradient to overcome the shared model
inconsistency across clients. Theoretically, we provide convergence analysis of
both algorithms in the general non-convex setting for decentralized partial
model training in PFL. Our experiments on several real-world data with various
data partition settings demonstrate that (i) decentralized training is more
suitable for partial personalization, which results in state-of-the-art (SOTA)
accuracy compared with the SOTA PFL baselines; (ii) the shared parameters with
proper perturbation make partial personalized FL more suitable for
decentralized training, where DFedSalt achieves most competitive performance.
