Differentially private stochastic gradient descent (DP-SGD) is the canonical algorithm for private deep learning. While it is known that its privacy analysis is tight in the worst-case, several empirical results suggest that when training on common benchmark datasets, the models obtained leak significantly less privacy for many datapoints. In this paper, we develop a new analysis for DP-SGD that captures the intuition that points with similar neighbors in the dataset enjoy better privacy than outliers. Formally, this is done by modifying the per-step privacy analysis of DP-SGD to introduce a dependence on the distribution of model updates computed from a training dataset. We further develop a new composition theorem to effectively use this new per-step analysis to reason about an entire training run. Put all together, our evaluation shows that this novel DP-SGD analysis allows us to now formally show that DP-SGD leaks significantly less privacy for many datapoints. In particular, we observe that correctly classified points obtain better privacy guarantees than misclassified points.

本文发展了一种新的DP-SGD分析方法，该算法能够更好地处理训练数据集中许多数据点的隐私泄露问题，具有更好的隐私保障，特别是对正确分类的数据点而言。

梯度看起来相似：DP-SGD中的敏感性经常被高估