Privacy protection of users' entire contribution of samples is important in
distributed systems. The most effective approach is the two-stage scheme, which
finds a small interval first and then gets a refined estimate by clipping
samples into the interval. However, the clipping operation induces bias, which
is serious if the sample distribution is heavy-tailed. Besides, users with
large local sample sizes can make the sensitivity much larger, thus the method
is not suitable for imbalanced users. Motivated by these challenges, we propose
a Huber loss minimization approach to mean estimation under user-level
differential privacy. The connecting points of Huber loss can be adaptively
adjusted to deal with imbalanced users. Moreover, it avoids the clipping
operation, thus significantly reducing the bias compared with the two-stage
approach. We provide a theoretical analysis of our approach, which gives the
noise strength needed for privacy protection, as well as the bound of mean
squared error. The result shows that the new method is much less sensitive to
the imbalance of user-wise sample sizes and the tail of sample distributions.
Finally, we perform numerical experiments to validate our theoretical analysis.

在分布式系统中，用户整体样本的隐私保护是很重要的。我们提出了基于 Huber loss 最小化的方法来进行用户级差分隐私下的均值估计，通过自适应调整 Huber loss 的连接点来处理不平衡的用户，避免了剪辑操作，大大减少了误差。通过理论分析和数值实验证实了我们的方法。

基于 Huber 损失的用户级差分隐私均值估计方法

A Huber Loss Minimization Approach to Mean Estimation under User-level  Differential Privacy

Federated learning systems are susceptible to adversarial attacks. To combat
this, we introduce a novel aggregator based on Huber loss minimization, and
provide a comprehensive theoretical analysis. Under independent and identically
distributed (i.i.d) assumption, our approach has several advantages compared to
existing methods. Firstly, it has optimal dependence on $\epsilon$, which
stands for the ratio of attacked clients. Secondly, our approach does not need
precise knowledge of $\epsilon$. Thirdly, it allows different clients to have
unequal data sizes. We then broaden our analysis to include non-i.i.d data,
such that clients have slightly different distributions.

联邦学习系统易受到对抗攻击，本研究基于 Huber 损失最小化引入了一种新型聚合器，并进行了全面的理论分析，相比现有方法，我们的方法在独立同分布的假设下具有几个优势，包括对被攻击客户端比例（ε）具有最优依赖性，不需要对 ε 进行精确的了解，允许不同客户端具有不均等的数据规模，此外，我们还拓展了分析范围，包括非独立同分布的数据，即客户端拥有略有不同的分布。