This paper establishes the equivalence between Local Differential Privacy (LDP) and a global limit on learning any knowledge about an object. However, an output from an LDP query is not necessarily required to provide exact amount of knowledge equal to the upper bound of the learning limit. Since the amount of knowledge gain should be proportional to the incurred privacy loss, the traditional approach of using DP guarantee to measure privacy loss can occasionally overestimate the actual privacy loss. This is especially problematic in privacy accounting in LDP, where privacy loss is computed by accumulating the DP guarantees. To address this issue, this paper introduces the concept of \textit{realized privacy loss}, which measures the actual knowledge gained by the analyst after a query, as a more accurate measure of privacy loss. The realized privacy loss is integrated into the privacy accounting of fully adaptive composition, where an adversary adaptively selects queries based on previous results. Bayesian Privacy Filter is implemented to continually accept queries until the realized privacy loss of the composed queries equals the DP guarantee of the composition, allowing the full utilization of the privacy budget. Tracking the realized privacy loss during the composition is achieved through Bayesian Privacy Odometer, and the gap between the privacy budget and the realized privacy loss measures the leeway of the DP guarantee for future queries. A branch-and-bound method is devised to enable the Bayesian Privacy Filter to safeguard objects with continuous values. The Bayesian Privacy Filter is proven to be at least as efficient as the basic composition, and more efficient if the queries are privacy-loss compactible. Experimental results indicate that Bayesian Privacy Filter outperforms the basic composition by a factor of one to four when composing linear and logistic regressions.

翻译：本文建立了本地差分隐私与关于对象知识学习的全局限制之间的等价关系。然而，本地差分隐私查询的输出并非必然要求提供等于学习上限的精确知识量。由于知识增益量应与隐私损失量成比例，传统使用差分隐私保证来衡量隐私损失的方法有时会高估实际隐私损失。这一问题在通过累加差分隐私保证计算隐私损失的本地差分隐私核算中尤为突出。为解决此问题，本文引入"实际隐私损失"概念，通过衡量分析者在查询后实际获得的知识量来更精确地度量隐私损失。该实际隐私损失被集成至完全自适应组合的隐私核算中，其中敌手基于先前结果自适应选择查询。通过实现贝叶斯隐私过滤器持续接收查询，直至组合查询的实际隐私损失等于组合的差分隐私保证，从而允许隐私预算的充分利用。组合过程中通过贝叶斯隐私里程表追踪实际隐私损失，而隐私预算与实际隐私损失之间的差值则衡量未来查询的差分隐私保证余量。针对连续值对象的保护，本文设计了分支定界法使贝叶斯隐私过滤器得以适用。理论证明，贝叶斯隐私过滤器至少与基础组合同样高效，若查询具有隐私损失可压缩性则效率更高。实验结果表明，在线性回归与逻辑回归的组合过程中，贝叶斯隐私过滤器的效率为基础组合的一至四倍。