The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation

We consider training models on private data that is distributed across user devices. To ensure privacy, we add on-device noise and use secure aggregation so that only the noisy sum is revealed to the server. We present a comprehensive end-to-end system, which appropriately discretizes the data and adds discrete Gaussian noise before performing secure aggregation. We provide a novel privacy analysis for sums of discrete Gaussians. We also analyze the effect of rounding the input data and the modular summation arithmetic. Our theoretical guarantees highlight the complex tension between communication, privacy, and accuracy. Our extensive experimental results demonstrate that our solution is essentially able to achieve a comparable accuracy to central differential privacy with 16 bits of precision per value

Optimal State Estimation with Measurements Corrupted by Laplace Noise

Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the state is approximated using a randomized method. The method relies on that the Laplace noise can be rewritten as Gaussian noise scaled by Rayleigh random variable. The probability of the event that the distance between the approximation and the best estimate is smaller than a constant is determined as function of the number of parallel Kalman filters that is used in the randomized method. This estimator is then compared with the optimal linear estimator, the maximum a posteriori (MAP) estimate of the state, and the particle filter