Lower Bounds for Differential Privacy in Continual Observation and Online Threshold Queries

Khái niệm cốt lõi

The authors present new lower bounds for differential privacy in continual observation and online threshold queries, challenging existing upper bounds.

Tóm tắt

The content discusses the challenges of maintaining privacy over time, focusing on the private counter problem and its implications. It introduces new lower bounds that extend to online threshold queries, highlighting separations between private and non-private online learning models.
The authors use Ramsey theory to prove their lower bounds, showcasing the complexity of ensuring differential privacy in evolving data scenarios. The content emphasizes the importance of understanding error dependencies on total time steps and event numbers.
Through detailed proofs and examples, the authors demonstrate the intricacies of maintaining privacy in continual observation settings, shedding light on the limitations of current algorithms.

Thống kê

Dwork et al. (2015) showed an upper bound of O(log(T) + log2(n)).
Henzinger et al. (2023) showed a lower bound of Ω(min{log n, log T}).
The known upper bound for online counters is O(min{n, log T + log2(n)}).
The prior lower bound is Ω(min{log T, log n}) by Henzinger et al. (2023).
For every T ≥ 1, let n ≤ 1/2 log(T) and δ ≤ 1/100n. Any (0.1, δ)-DP algorithm for the online counter problem with n events over T time steps must incur ℓ∞-error of Ω(n) with constant probability.

Trích dẫn

Thông tin chi tiết chính được chắt lọc từ

Lower Bounds for Differential Privacy Under Continual Observation and Online Threshold Queries

by Edit... lúc arxiv.org 03-04-2024

https://arxiv.org/pdf/2403.00028.pdf

Yêu cầu sâu hơn

How can these new lower bounds impact the development of future differential privacy algorithms

The new lower bounds for differential privacy presented in the context can have a significant impact on the development of future algorithms in this field. By establishing tighter lower bounds, researchers and developers are provided with clearer guidelines on the limitations and challenges that need to be addressed when designing differential privacy mechanisms. These lower bounds serve as benchmarks for evaluating the performance and effectiveness of new algorithms, pushing innovators to create more robust and efficient solutions.

What are some potential real-world applications where these findings could be crucial

These findings could be crucial in various real-world applications where data privacy is paramount. For example, in healthcare settings where sensitive patient information needs to be protected while still allowing for analysis and research, these lower bounds can guide the development of secure systems that maintain individual privacy. Additionally, in financial institutions handling customer data or government agencies dealing with citizen information, implementing differential privacy algorithms based on these lower bounds can ensure compliance with regulations while enabling valuable insights from data analysis.

How do these results contribute to our understanding of privacy-preserving technologies beyond traditional methods

The results contribute significantly to our understanding of privacy-preserving technologies beyond traditional methods by highlighting the complexities involved in ensuring differential privacy under continual observation and online scenarios. By demonstrating tight lower bounds for specific problems like private counters and threshold queries, these findings shed light on the inherent challenges faced when maintaining individual confidentiality over time or when responding to sequential queries without compromising overall system integrity. This deeper understanding paves the way for more sophisticated approaches to safeguarding sensitive data across various domains effectively.