In privacy-preserving data analysis, many procedures and algorithms are structured as compositions of multiple private building blocks. As such, an important question is how to efficiently compute the overall privacy loss under composition. This paper introduces the Edgeworth Accountant, an analytical approach to composing differential privacy guarantees for private algorithms. Leveraging the $f$-differential privacy framework, the Edgeworth Accountant accurately tracks privacy loss under composition, enabling a closed-form expression of privacy guarantees through privacy-loss log-likelihood ratios (PLLRs). As implied by its name, this method applies the Edgeworth expansion to estimate and define the probability distribution of the sum of the PLLRs. Furthermore, by using a technique that simplifies complex distributions into simpler ones, we demonstrate the Edgeworth Accountant's applicability to any noise-addition mechanism. Its main advantage is providing $(ε, δ)$-differential privacy bounds that are non-asymptotic and do not significantly increase computational cost. This feature sets it apart from previous approaches, in which the running time increases with the number of mechanisms under composition. We conclude by showing how our Edgeworth Accountant offers accurate estimates and tight upper and lower bounds on $(ε, δ)$-differential privacy guarantees, especially tailored for training private models in deep learning and federated analytics.

翻译：在隐私保护数据分析中，许多程序和算法被构建为多个隐私构建块的组合。因此，一个重要问题是如何高效地计算组合下的整体隐私损失。本文介绍了Edgeworth会计，一种用于组合私有算法差分隐私保证的解析方法。该方法利用$f$-差分隐私框架，精确追踪组合下的隐私损失，通过隐私损失对数似然比（PLLR）实现隐私保证的闭式表达。如其名称所示，该方法应用Edgeworth展开来估计和定义PLLR之和的概率分布。此外，通过使用一种将复杂分布简化为更简单分布的技术，我们证明了Edgeworth会计适用于任何噪声添加机制。其主要优势在于提供非渐近且不会显著增加计算成本的$(ε, δ)$-差分隐私边界。这一特点使其区别于以往方法，后者的运行时间会随组合机制数量增加而增长。最后，我们展示了Edgeworth会计如何为$(ε, δ)$-差分隐私保证提供精确估计及紧致的上下界，尤其适用于深度学习和联邦分析中的私有模型训练。