Separating Oblivious and Adaptive Differential Privacy under Continual Observation

TL;DR

This paper demonstrates a fundamental difference between oblivious and adaptive differential privacy in streaming models, showing an explicit problem separation with significant implications for privacy guarantees.

Contribution

It provides the first explicit separation between oblivious and adaptive differential privacy in continual observation, using a problem based on correlated vector queries.

Findings

Oblivious setting allows accurate privacy-preserving streaming for exponentially many steps.

Adaptive setting fails to maintain accuracy after a constant number of steps.

The separation is based on the correlated vector queries problem.

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 $(\varepsilon,\delta)$-DP adaptive algorithm fails to be accurate after releasing output for only a constant number of time steps.