Tight Data Access Bounds for Private Top-$k$ Selection

Hao Wu, Olga Ohrimenko, Anthony Wirth
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:37635-37655, 2023.

Abstract

We study the top-$k$ selection problem under the differential privacy model: $m$ items are rated according to votes of a set of clients. We consider a setting in which algorithms can retrieve data via a sequence of accesses, each either a random access or a sorted access; the goal is to minimize the total number of data accesses. Our algorithm requires only $O(\sqrt{mk})$ expected accesses: to our knowledge, this is the first sublinear data-access upper bound for this problem. Our analysis also shows that the well-known exponential mechanism requires only $O(\sqrt{m})$ expected accesses. Accompanying this, we develop the first lower bounds for the problem, in three settings: only random accesses; only sorted accesses; a sequence of accesses of either kind. We show that, to avoid $\Omega(m)$ access cost, supporting both kinds of access is necessary, and that in this case our algorithm’s access cost is optimal.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-wu23q, title = {Tight Data Access Bounds for Private Top-$k$ Selection}, author = {Wu, Hao and Ohrimenko, Olga and Wirth, Anthony}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {37635--37655}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/wu23q/wu23q.pdf}, url = {https://proceedings.mlr.press/v202/wu23q.html}, abstract = {We study the top-$k$ selection problem under the differential privacy model: $m$ items are rated according to votes of a set of clients. We consider a setting in which algorithms can retrieve data via a sequence of accesses, each either a random access or a sorted access; the goal is to minimize the total number of data accesses. Our algorithm requires only $O(\sqrt{mk})$ expected accesses: to our knowledge, this is the first sublinear data-access upper bound for this problem. Our analysis also shows that the well-known exponential mechanism requires only $O(\sqrt{m})$ expected accesses. Accompanying this, we develop the first lower bounds for the problem, in three settings: only random accesses; only sorted accesses; a sequence of accesses of either kind. We show that, to avoid $\Omega(m)$ access cost, supporting both kinds of access is necessary, and that in this case our algorithm’s access cost is optimal.} }
Endnote
%0 Conference Paper %T Tight Data Access Bounds for Private Top-$k$ Selection %A Hao Wu %A Olga Ohrimenko %A Anthony Wirth %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-wu23q %I PMLR %P 37635--37655 %U https://proceedings.mlr.press/v202/wu23q.html %V 202 %X We study the top-$k$ selection problem under the differential privacy model: $m$ items are rated according to votes of a set of clients. We consider a setting in which algorithms can retrieve data via a sequence of accesses, each either a random access or a sorted access; the goal is to minimize the total number of data accesses. Our algorithm requires only $O(\sqrt{mk})$ expected accesses: to our knowledge, this is the first sublinear data-access upper bound for this problem. Our analysis also shows that the well-known exponential mechanism requires only $O(\sqrt{m})$ expected accesses. Accompanying this, we develop the first lower bounds for the problem, in three settings: only random accesses; only sorted accesses; a sequence of accesses of either kind. We show that, to avoid $\Omega(m)$ access cost, supporting both kinds of access is necessary, and that in this case our algorithm’s access cost is optimal.
APA
Wu, H., Ohrimenko, O. & Wirth, A.. (2023). Tight Data Access Bounds for Private Top-$k$ Selection. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:37635-37655 Available from https://proceedings.mlr.press/v202/wu23q.html.

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