Privacy-Resolution Tradeoff for Adaptive Noisy Twenty Questions Estimation

2026-01-23

AI Summary

This work addresses the fundamental challenge of balancing privacy preservation with high-accuracy estimation in the adaptive noisy twenty questions problem. The authors propose a two-stage private adaptive querying mechanism that effectively reconciles privacy and estimation accuracy under noisy conditions. For the first time, the privacy–resolution trade-off analysis is extended to noisy settings, and the impact of privacy constraints on estimation performance is rigorously quantified using both non-asymptotic and second-order asymptotic methods. The proposed mechanism outperforms existing private querying strategies in both noisy and noiseless scenarios, achieving state-of-the-art estimation performance while guaranteeing differential privacy.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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).

Problem

• privacy-resolution tradeoff
• adaptive querying
• noisy twenty questions
• estimation
• privacy concerns

Innovation

• privacy-resolution tradeoff
• adaptive querying
• noisy twenty questions
• private estimation
• two-stage query procedure