Paper:
Distributed Learning without Distress: Privacy-Preserving Empirical Risk Minimization
Distributed learning allows a group of independent data owners to collaboratively learn a model over their data sets without exposing their private data. We present a distributed learning approach that combines differential privacy with secure multiparty computation. We explore two popular methods of differential privacy, output perturbation and gradient perturbation, and advance the state-of-the-art for both methods in the distributed learning setting. In our output perturbation method, the parties combine local models within a secure computation and then add the required differential privacy noise before revealing the model. In our gradient perturbation method, the data owners collaboratively train a global model via an iterative learning algorithm. At each iteration, the parties aggregate their local gradients within a secure computation, adding sufficient noise to ensure privacy before the gradient updates are revealed. For both methods, we show that the noise can be reduced in the multi-party setting by adding the noise inside the secure computation after aggregation, asymptotically improving upon the best previous results. Experiments on real world data sets demonstrate that our methods provide substantial utility gains for typical privacy requirements.

Review:
The paper is about learning in a decentralized setting where parties have their own dataset and learn privately a global model. Privacy is usually guaranteed either by cryptographic procedures (secure multi party computation, MPC) or by introducing noise and theoretically analyzed in the framework of differential privacy (DP). Following Pathak et al [39], the paper combines MPC and DP. But the main contribution is to reduce the noise by a factor sqrt(m) using two different techniques: one from Chauduri et al [10] and one from Bun and Steike [6]. The paper considers two settings, output perturbation and gradient perturbation.   In the output perturbation scheme, the parties securely send their model learned locally to a central server, the server aggregates (averages) the models to build a joined model and then adds noise before releasing it. The average is privately computed in the MPC protocol. The approach is therefore very similar to the one of Pathak. The contribution in this part of the paper is to use a bound proved in Chauduri et al [10] in the proof that evaluates the needed noise to be \epsilon-DP.  In the gradient perturbation scheme, noise is introduced at every gradient step, after averaging the gradients, and before sending a new model back to the parties. Therefore, a general result is obtained using composition results in DP. The paper relies on zero concentrated DP for a more efficient combination step (Bun and Steike [6]).  The new bounds improves also the impact of noise in the true and empirical risks (and therefore it is important for associated ERM problems). Most of the proofs are not original (adapted from Chauduri and Monteleoni [9]) but  easy to follow and clearly exposed.     The paper is clearly written. The authors have correctly explained the motivations and have honestly indicated at the core of their contribution, to whom this or that result was attributed. Detailed proofs are given in the appendix.   The authors claim in different points of the paper that the benefit is explained by the fact that they add noise inside the MPC. This is not clear for me because in each scheme, the noise is introduced after model aggregation (so it could be "after" rather than "inside").   In conclusion, the paper improves the known bounds and shows theoretically and experimentally the benefits of the proposed algorithms. The significance is moderated by the fact that the results are obtained from small adaptations of the known techniques using each time another work. But I think that the paper is clearly written and the results are interesting.    Technical:  - l133-134 is difficult to understand (almost false). I think that the authors want to  say that Z is concentrated around 0 and then it becomes unlikely to distinguish D from D'.  - I am not sure that the comparison with Pathak et al is fair enough because they use the l1 norm to bound the difference between two models learned from closeby by datasets     UPDATE:  "The key difference is whether the noise is added before or after the models are aggregated." Indeed, you're right and it is more clear to say after r before aggregation than "inside/within" (because the MPC is not really modified).