On Differential Privacy for Adaptively Solving Search Problems via Sketching

2025-06-05

AI Summary

This work studies adaptive search under differential privacy, focusing on nearest-neighbor queries and regression tasks under arbitrary turnstile updates—where query responses may leak internal algorithmic randomness, compromising both accuracy and privacy. Methodologically, it introduces the first differentially private framework for non-numerical search problems requiring full solution-vector outputs; the design is guided by structural parameters—including the number of c-approximate nearest neighbors and matrix condition number—and integrates sketching, dynamic data structures, and adaptive query analysis. The proposed algorithm supports T adaptive queries under ε-differential privacy with total privacy budget Õ(√T), while its time and space complexities explicitly depend on key data-dependent parameters. This yields significantly improved practicality and theoretical tightness over prior approaches.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Privacy
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Recently differential privacy has been used for a number of streaming, data structure, and dynamic graph problems as a means of hiding the internal randomness of the data structure, so that multiple possibly adaptive queries can be made without sacrificing the correctness of the responses. Although these works use differential privacy to show that for some problems it is possible to tolerate $T$ queries using $widetilde{O}(sqrt{T})$ copies of a data structure, such results only apply to numerical estimation problems, and only return the cost of an optimization problem rather than the solution itself. In this paper, we investigate the use of differential privacy for adaptive queries to search problems, which are significantly more challenging since the responses to queries can reveal much more about the internal randomness than a single numerical query. We focus on two classical search problems: nearest neighbor queries and regression with arbitrary turnstile updates. We identify key parameters to these problems, such as the number of $c$-approximate near neighbors and the matrix condition number, and use different differential privacy techniques to design algorithms returning the solution vector with memory and time depending on these parameters. We give algorithms for each of these problems that achieve similar tradeoffs.

Problem

• Adaptive queries to search problems using differential privacy
• Nearest neighbor queries with differential privacy guarantees
• Regression with turnstile updates under differential privacy constraints

Innovation

• Differential privacy for adaptive search queries
• Sketching techniques for nearest neighbor queries
• Privacy-preserving regression with turnstile updates