  Federated learning enables multiple participants to collaboratively train a
model without aggregating the training data. Although the training data are
kept within each participant and the local gradients can be securely
synthesized, recent studies have shown that such privacy protection is
insufficient. The global model parameters that have to be shared for
optimization are susceptible to leak information about training data. In this
work, we propose Confined Gradient Descent (CGD) that enhances privacy of
federated learning by eliminating the sharing of global model parameters. CGD
exploits the fact that a gradient descent optimization can start with a set of
discrete points and converges to another set at the neighborhood of the global
minimum of the objective function. It lets the participants independently train
on their local data, and securely share the sum of local gradients to benefit
each other. We formally demonstrate CGD's privacy enhancement over traditional
FL. We prove that less information is exposed in CGD compared to that of
traditional FL. CGD also guarantees desired model accuracy. We theoretically
establish a convergence rate for CGD. We prove that the loss of the proprietary
models learned for each participant against a model learned by aggregated
training data is bounded. Extensive experimental results on two real-world
datasets demonstrate the performance of CGD is comparable with the centralized
learning, with marginal differences on validation loss (mostly within 0.05) and
accuracy (mostly within 1%).
