  Data privacy and security becomes a major concern in building machine
learning models from different data providers. Federated learning shows promise
by leaving data at providers locally and exchanging encrypted information. This
paper studies the vertical federated learning structure for logistic regression
where the data sets at two parties have the same sample IDs but own disjoint
subsets of features. Existing frameworks adopt the first-order stochastic
gradient descent algorithm, which requires large number of communication
rounds. To address the communication challenge, we propose a quasi-Newton
method based vertical federated learning framework for logistic regression
under the additively homomorphic encryption scheme. Our approach can
considerably reduce the number of communication rounds with a little additional
communication cost per round. Numerical results demonstrate the advantages of
our approach over the first-order method.
