  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.
