Subset-Based Instance Optimality in Private Estimation

• URL: http://arxiv.org/abs/2303.01262v3
• Date: Wed, 29 May 2024 01:37:23 GMT
• Title: Subset-Based Instance Optimality in Private Estimation
• Authors: Travis Dick, Alex Kulesza, Ziteng Sun, Ananda Theertha Suresh,
• Abstract summary: We show how to construct private algorithms that achieve our notion of instance optimality when estimating a broad class of dataset properties. Our algorithm simultaneously matches or exceeds the performance of existing algorithms under a range of distributional assumptions.
• Score: 23.173651165908282
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new definition of instance optimality for differentially private estimation algorithms. Our definition requires an optimal algorithm to compete, simultaneously for every dataset $D$, with the best private benchmark algorithm that (a) knows $D$ in advance and (b) is evaluated by its worst-case performance on large subsets of $D$. That is, the benchmark algorithm need not perform well when potentially extreme points are added to $D$; it only has to handle the removal of a small number of real data points that already exist. This makes our benchmark significantly stronger than those proposed in prior work. We nevertheless show, for real-valued datasets, how to construct private algorithms that achieve our notion of instance optimality when estimating a broad class of dataset properties, including means, quantiles, and $\ell_p$-norm minimizers. For means in particular, we provide a detailed analysis and show that our algorithm simultaneously matches or exceeds the asymptotic performance of existing algorithms under a range of distributional assumptions.

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