We revisit noisy twenty questions estimation and study the privacy-resolution tradeoff for adaptive query procedures. Specifically, in twenty questions estimation, there are two players: an oracle and a questioner. The questioner aims to estimate target variables by posing queries to the oracle that knows the variables and using noisy responses to form reliable estimates. Typically, there are adaptive and non-adaptive query procedures. In adaptive querying, one designs the current query using previous queries and their noisy responses while in non-adaptive querying, all queries are posed simultaneously. Generally speaking, adaptive query procedures yield better performance. However, adaptive querying leads to privacy concerns, which were first studied by Tsitsiklis, Xu and Xu (COLT 2018) and by Xu, Xu and Yang (AISTATS 2021) for the noiseless case, where the oracle always provides correct answers to queries. In this paper, we generalize the above results to the more practical noisy case, by proposing a two-stage private query procedure, analyzing its non-asymptotic and second-order asymptotic achievable performance and discussing the impact of privacy concerns. Furthermore, when specialized to the noiseless case, our private query procedure achieves better performance than above-mentioned query procedures (COLT 2018, AISTATS 2021).

翻译：本文重新审视噪声二十问题估计，并研究自适应查询过程中的隐私-分辨率权衡。具体而言，在二十问题估计中，存在两个参与者：应答者与提问者。提问者旨在通过向掌握目标变量的应答者提出查询，并利用含噪声的响应构建可靠估计。通常存在自适应与非自适应两种查询策略：在自适应查询中，当前查询的设计依赖于先前查询及其噪声响应；而在非自适应查询中，所有查询同时提出。一般而言，自适应查询策略具有更优的性能表现。然而，自适应查询会引发隐私泄露问题，该问题首先由Tsitsiklis、Xu和Xu（COLT 2018）以及Xu、Xu和Yang（AISTATS 2021）针对无噪声情形（即应答者始终提供正确响应）进行了研究。本文通过提出一种两阶段隐私保护查询策略，分析其非渐近及二阶渐近可达性能，并探讨隐私约束的影响，将上述结果推广至更具实际意义的含噪声场景。此外，当应用于无噪声特例时，本文提出的隐私保护查询策略较前述研究（COLT 2018, AISTATS 2021）取得了更优的性能。