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

Authors: Hao Wu, Olga Ohrimenko, Anthony Wirth

ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical 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(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(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 Ω(m) access cost, supporting both kinds of access is necessary, and that in this case our algorithm s access cost is optimal.
Researcher Affiliation Academia 1School of Computing and Information Systems, The University of Melbourne. Correspondence to: Hao Wu <whw4@student.unimelb.edu.au>, Olga Ohrimenko <oohrimenko@unimelb.edu.au>, Anthony Wirth <awirth@unimelb.edu.au>.
Pseudocode Yes Algorithm 1 Threshold Algorithm ATA (Fagin et al., 2003); Algorithm 2 Private Top-k Algorithm M; Algorithm 3 Private Threshold Algorithm APriv TA; Algorithm 4 Algorithm Aoracle.
Open Source Code No The paper does not provide any explicit statements or links indicating that source code for the described methodology is publicly available.
Open Datasets No The paper is theoretical and does not use real-world or simulated datasets that are made publicly available. It defines abstract data models (e.g., 'Let C .= {1, . . . , m} be a set of m items, and U .= {1, . . . , n} be a set of n clients.').
Dataset Splits No The paper is theoretical and does not involve empirical data splits for training, validation, or testing.
Hardware Specification No The paper is theoretical and does not describe any specific hardware used for experiments.
Software Dependencies No The paper is theoretical and does not list any specific software dependencies with version numbers required for reproducibility.
Experiment Setup No The paper is theoretical and does not describe an experimental setup with hyperparameters or training settings.