Separating Oblivious and Adaptive Differential Privacy under Continual Observation

2026-03-11

AI Summary

This work investigates the gap in utility between forgetful differential privacy and adaptive differential privacy under the continual observation model. Focusing on the correlated vector query problem introduced by Bun et al., we design an (ε,0)-differentially private algorithm and establish, for the first time, a rigorous separation between the accuracy guarantees achievable under these two privacy notions. Specifically, our algorithm achieves high accuracy over an exponentially large number of time steps in the forgetful setting, whereas in the adaptive setting, any (ε,δ)-differentially private algorithm can maintain accuracy only for a constant number of time steps. This result resolves an open problem posed at ICML 2023 and reveals a fundamental distinction between the two privacy frameworks in dynamic data environments.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Sequential Decision Making
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We resolve an open question of Jain, Raskhodnikova, Sivakumar, and Smith (ICML 2023) by exhibiting a problem separating differential privacy under continual observation in the oblivious and adaptive settings. The continual observation (a.k.a. continual release) model formalizes privacy for streaming algorithms, where data is received over time and output is released at each time step. In the oblivious setting, privacy need only hold for data streams fixed in advance; in the adaptive setting, privacy is required even for streams that can be chosen adaptively based on the streaming algorithm's output. We describe the first explicit separation between the oblivious and adaptive settings. The problem showing this separation is based on the correlated vector queries problem of Bun, Steinke, and Ullman (SODA 2017). Specifically, we present an $(\varepsilon,0)$-DP algorithm for the oblivious setting that remains accurate for exponentially many time steps in the dimension of the input. On the other hand, we show that every $(\varepsilon,δ)$-DP adaptive algorithm fails to be accurate after releasing output for only a constant number of time steps.

Problem

• differential privacy
• continual observation
• oblivious setting
• adaptive setting
• privacy separation

Innovation

• continual observation
• differential privacy
• oblivious vs adaptive
• streaming algorithms
• correlated vector queries