标题： 差分隐私下指数分布的学习：自适应算法和紧界 显示英文标题

标题： Differentially Private Learning of Exponential Distributions: Adaptive Algorithms and Tight Bounds

摘要： 我们研究在差分隐私下的指数分布学习问题。 给定 $n$个来自 $\mathrm{Exp}(\lambda)$ 的独立同分布样本，目标是私密地估计 $\lambda$，使得学习到的分布与真实分布在总变分距离上接近。 我们提出了两种互补的纯差分隐私算法：一种通过截断和拉普拉斯噪声适应经典的最大似然估计器，而另一种利用了 $(1-1/e)$-分位数等于 $1/\lambda$的事实。 每种方法在不同的情况下表现优异，我们将它们结合成一个自适应的双优算法，实现了对所有 $\lambda$的近最优样本复杂度。 我们进一步通过对数变换将方法扩展到帕累托分布，使用打包和群隐私证明了几乎匹配的下界\cite{Karwa2017FiniteSD}，并展示了近似$(\epsilon,\delta)$-DP 如何消除对外部提供边界的需求。 这些结果共同给出了差分隐私下指数分布学习的第一个紧致表征，并展示了自适应策略在重尾分布中的强大能力。 显示英文摘要

摘要： We study the problem of learning exponential distributions under differential privacy. Given $n$ i.i.d.\ samples from $\mathrm{Exp}(\lambda)$, the goal is to privately estimate $\lambda$ so that the learned distribution is close in total variation distance to the truth. We present two complementary pure DP algorithms: one adapts the classical maximum likelihood estimator via clipping and Laplace noise, while the other leverages the fact that the $(1-1/e)$-quantile equals $1/\lambda$. Each method excels in a different regime, and we combine them into an adaptive best-of-both algorithm achieving near-optimal sample complexity for all $\lambda$. We further extend our approach to Pareto distributions via a logarithmic reduction, prove nearly matching lower bounds using packing and group privacy \cite{Karwa2017FiniteSD}, and show how approximate $(\epsilon,\delta)$-DP removes the need for externally supplied bounds. Together, these results give the first tight characterization of exponential distribution learning under DP and illustrate the power of adaptive strategies for heavy-tailed laws.