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.

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.

Neural Information Processing Systems http://nips.cc/

Many recent works have shown that adversarial examples that fool classifiers can be found by minimally perturbing a normal input. Recent theoretical results, starting with Gilmer et al. (2018b), show that if the inputs are drawn from a concentrated metric probability space, then adversarial examples with small perturbation are inevitable. A concentrated space has the property that any subset with Ω(1) (e.g., 1/100) measure, according to the imposed distribution, has small distance to almost all (e.g., 99/100) of the points in the space. It is not clear, however, whether these theoretical results apply to actual distributions such as images. This paper presents a method for empirically measuring and bounding the concentration of a concrete dataset which is proven to converge to the actual concentration.