arXiv:2310.13367v3 Announce Type: replace-cross Abstract: Vertical federated learning has garnered significant attention as it allows clients to train machine learning models collaboratively without sharing local data, which protects the client's local private data. However, existing VFL methods face challenges when dealing with heterogeneous local models among participants, which affects optimization convergence and generalization. To address this challenge, this paper proposes a novel approach called Vertical federated learning for training multiple Heterogeneous models (VFedMH). VFedMH focuses on aggregating the local embeddings of each participant's knowledge during forward propagation. To protect the participants' local embedding values, we propose an embedding protection method based on lightweight blinding factors. In particular, participants obtain local embedding using local heterogeneous models. Then the passive party, who owns only features of the sample, injects the blinding factor into the local embedding and sends it to the active party. The active party aggregates local embeddings to obtain global knowledge embeddings and sends them to passive parties. The passive parties then utilize the global embeddings to propagate forward on their local heterogeneous networks. However, the passive party does not own the sample labels, so the local model gradient cannot be calculated locally. To overcome this limitation, the active party assists the passive party in computing its local heterogeneous model gradients. Then, each participant trains their local model using the heterogeneous model gradients. The objective is to minimize the loss value of their respective local heterogeneous models. Extensive experiments are conducted to demonstrate that VFedMH can simultaneously train multiple heterogeneous models with heterogeneous optimization and outperform some recent methods in model performance.