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arXiv · 2411.09552

Faster Differentially Private Top-$k$ Selection: A Joint Exponential Mechanism with Pruning

Hao WU·Hanwen Zhang
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Abstract

We study the differentially private top-$k$ selection problem, aiming to identify a sequence of $k$ items with approximately the highest scores from $d$ items. Recent work by Gillenwater et al. (ICML '22) employs a direct sampling approach from the vast collection of $d^{\,\Theta(k)}$ possible length-$k$ sequences, showing superior empirical accuracy compared to previous pure or approximate differentially private methods. Their algorithm has a time and space complexity of $\tilde{O}(dk)$. In this paper, we present an improved algorithm with time and space complexity $O(d + k^2 / \epsilon \cdot \ln d)$, where $\epsilon$ denotes the privacy parameter. Experimental results show that our algorithm runs orders of magnitude faster than their approach, while achieving similar empirical accuracy.

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Hao WU, Hanwen Zhang. 2024-11-14. Faster Differentially Private Top-$k$ Selection: A Joint Exponential Mechanism with Pruning. https://doi.org/10.52202/079017-2266

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