  Distributed privacy-preserving regression schemes have been developed and
extended in various fields, where multiparty collaboratively and privately run
optimization algorithms, e.g., Gradient Descent, to learn a set of optimal
parameters. However, traditional Gradient-Descent based methods fail to solve
problems which contains objective functions with L1 regularization, such as
Lasso regression. In this paper, we present Federated Coordinate Descent, a new
distributed scheme called FCD, to address this issue securely under multiparty
scenarios. Specifically, through secure aggregation and added perturbations,
our scheme guarantees that: (1) no local information is leaked to other
parties, and (2) global model parameters are not exposed to cloud servers. The
added perturbations can eventually be eliminated by each party to derive a
global model with high performance. We show that the FCD scheme fills the gap
of multiparty secure Coordinate Descent methods and is applicable for general
linear regressions, including linear, ridge and lasso regressions. Theoretical
security analysis and experimental results demonstrate that FCD can be
performed effectively and efficiently, and provide as low MAE measure as
centralized methods under tasks of three types of linear regressions on
real-world UCI datasets.
