Limits of Personalizing Differential Privacy Budgets

2026-05-13

AI Summary

This work investigates the practical utility gains of personalized differential privacy budgets in mean estimation tasks and demonstrates through theoretical analysis that such advantages are limited to at most a constant-factor improvement, contingent upon the choice of effective privacy budgets. To address this, we propose a simple thresholding operator that achieves near-optimal utility under arbitrary privacy requirements and derive a tight upper bound on performance in general settings. Empirical evaluations on hybrid public-private datasets across two distinct privacy scenarios confirm both the limited benefit of personalization and the alignment of observed performance with the established theoretical bounds.

Abstract

A key technical difficulty in differential privacy is selecting a privacy budget that satisfies privacy requirements while maximizing utility. A natural and well-studied workaround is to use personalized privacy budgets, which may differ across agents. In this paper, we show that personalized budgets come with major limitations and that for mean estimation, the dominant factor is not full personalization, but rather choosing the right effective privacy budget. This can be achieved through a simple thresholding operator that we describe. Compared with this thresholding baseline, the gains obtained by fully personalized mechanisms are limited. In particular, we precisely quantify the constant-factor improvement in settings with mixed private and public datasets and in private datasets with two levels of privacy requirements. We also establish upper bounds and identify regimes of maximal gain for arbitrary privacy requirements.

Problem

• differential privacy
• privacy budget
• personalization
• utility
• mean estimation

Innovation

• personalized differential privacy
• privacy budget
• thresholding operator
• mean estimation
• utility-privacy tradeoff