A unifying framework for differentially private sums under continual observation

Henzinger MH, Upadhyay J, Upadhyay S. 2024. A unifying framework for differentially private sums under continual observation. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2024, 995–1018.

Download (ext.)

Conference Paper | Published | English

Scopus indexed
Author
Henzinger, MonikaISTA ; Upadhyay, Jalaj; Upadhyay, Sarvagya

Corresponding author has ISTA affiliation

Abstract
We study the problem of maintaining a differentially private decaying sum under continual observation. We give a unifying framework and an efficient algorithm for this problem for any sufficiently smooth function. Our algorithm is the first differentially private algorithm that does not have a multiplicative error for polynomially decaying weights. Our algorithm improves on all prior works on differentially private decaying sums under continual observation and recovers exactly the additive error for the special case of continual counting from Henzinger et al. (SODA 2023) as a corollary. Our algorithm is a variant of the matrix mechanism whose error depends on the γ2 and γF norm of the underlying matrix. We give a constructive proof for an almost exact upper bound on the γ2 and γF norm and an almost tight lower bound on the γ2 norm for a large class of lower-triangular matrices. This is the first non-trivial lower bound for lower-triangular matrices whose non-zero entries are not all the same. It includes matrices for all continual decaying sums problems, resulting in an upper bound on the additive error of any differentially private decaying sums algorithm under continual observation. We also explore some implications of our result in discrepancy theory and operator algebra. Given the importance of the γ2 norm in computer science and the extensive work in mathematics, we believe our result will have further applications.
Publishing Year
Date Published
2024-01-04
Proceedings Title
Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Acknowledgement
This project has received funding from the European Research Council (ERC)under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No.101019564 “The Design of Modern Fully Dynamic Data Structures (MoDynStruct)” and the AustrianScience Fund (FWF) project Z 422-N, project “Static and Dynamic Hierarchical Graph Decompositions”, I 5982-N, andproject “Fast Algorithms for a Reactive Network Layer (ReactNet)”, P 33775-N, with additional funding from the netideeSCIENCE Stiftung, 2020–2024. JU’s research was funded by the Decanal Research Grant. We thank the anonymousreviewers for their useful feedback and pointing us to the results in Matousek et al
Volume
2024
Page
995-1018
Conference
SODA: Symposium on Discrete Algorithms
Conference Location
Alexandria, VA, United States
Conference Date
2024-01-07 – 2024-01-10
IST-REx-ID

Cite this

Henzinger MH, Upadhyay J, Upadhyay S. A unifying framework for differentially private sums under continual observation. In: Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms. Vol 2024. Society for Industrial and Applied Mathematics; 2024:995-1018. doi:10.1137/1.9781611977912.38
Henzinger, M. H., Upadhyay, J., & Upadhyay, S. (2024). A unifying framework for differentially private sums under continual observation. In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (Vol. 2024, pp. 995–1018). Alexandria, VA, United States: Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611977912.38
Henzinger, Monika H, Jalaj Upadhyay, and Sarvagya Upadhyay. “A Unifying Framework for Differentially Private Sums under Continual Observation.” In Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms, 2024:995–1018. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/1.9781611977912.38.
M. H. Henzinger, J. Upadhyay, and S. Upadhyay, “A unifying framework for differentially private sums under continual observation,” in Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms, Alexandria, VA, United States, 2024, vol. 2024, pp. 995–1018.
Henzinger MH, Upadhyay J, Upadhyay S. 2024. A unifying framework for differentially private sums under continual observation. Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2024, 995–1018.
Henzinger, Monika H., et al. “A Unifying Framework for Differentially Private Sums under Continual Observation.” Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2024, Society for Industrial and Applied Mathematics, 2024, pp. 995–1018, doi:10.1137/1.9781611977912.38.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data ISTA Research Explorer

Sources

arXiv 2307.08970

Search this title in

Google Scholar