Machine learning (ML) models trained by differentially private stochastic gradient descent (DP-SGD) has much lower utility than the non-private ones. To mitigate this degradation, we propose a DP Laplacian smoothing SGD (DP-LSSGD) for privacy-preserving ML. At the core of DP-LSSGD is the Laplace smoothing operator, which smooths out the Gaussian noise vector used in the Gaussian mechanism. Under the same amount of noise used in the Gaussian mechanism, DP-LSSGD attains the same differential privacy guarantee, but a strictly better utility guarantee, excluding an intrinsic term which is usually dominated by the other terms, for convex optimization than DP-SGD by a factor which is much less than one. In practice, DP-LSSGD makes training both convex and nonconvex ML models more efficient and enables the trained models to generalize better. For ResNet20, under the same strong differential privacy guarantee, DP-LSSGD can lift the testing accuracy of the trained private model by more than $8$\% compared with DP-SGD. The proposed algorithm is simple to implement and the extra computational complexity and memory overhead compared with DP-SGD are negligible. DP-LSSGD is applicable to train a large variety of ML models, including deep neural nets. The code is available at \url{https://github.com/BaoWangMath/DP-LSSGD}.

本研究提出DP-LSSGD，一种基于差分隐私的SGD算法，通过Laplacian smoothing减少噪音并保证同样的隐私保证，让训练凸和非凸机器学习模型更加稳定，同时使得模型泛化更好。

DP-LSSGD: 隐私保护ERM中提高效用的随机优化方法