  We address the problem of learning a machine learning model from training
data that originates at multiple data owners while providing formal privacy
guarantees regarding the protection of each owner's data. Existing solutions
based on Differential Privacy (DP) achieve this at the cost of a drop in
accuracy. Solutions based on Secure Multiparty Computation (MPC) do not incur
such accuracy loss but leak information when the trained model is made publicly
available. We propose an MPC solution for training DP models. Our solution
relies on an MPC protocol for model training, and an MPC protocol for
perturbing the trained model coefficients with Laplace noise in a
privacy-preserving manner. The resulting MPC+DP approach achieves higher
accuracy than a pure DP approach while providing the same formal privacy
guarantees. Our work obtained first place in the iDASH2021 Track III
competition on confidential computing for secure genome analysis.
