Adaptive Privacy Budgeting

TL;DR

The paper addresses adaptive privacy budgeting under generalized differential privacy to efficiently allocate a fixed privacy budget across multiple queries and users. It develops privacy filters based on stopping-time analysis to provide ex-ante GP/CGP guarantees and introduces iterative-elimination templates (PIE) to realize privacy savings, both in non-interactive and interactive settings. The framework is instantiated for core problems—range counting, Gaussian KDE, and $k$NN—with baseline and PIE variants that selectively withhold participation to reduce privacy loss while preserving utility. Empirical results on real datasets demonstrate meaningful privacy savings and improved or preserved accuracy across single and multiple-query scenarios, illustrating the practical impact of adaptive budgeting in privacy-sensitive analytics.

Abstract

We study the problem of adaptive privacy budgeting under generalized differential privacy. Consider the setting where each user $i\in [n]$ holds a tuple $x_i\in U:=U_1\times \dotsb \times U_T$, where $x_i(l)\in U_l$ represents the $l$-th component of their data. For every $l\in [T]$ (or a subset), an untrusted analyst wishes to compute some $f_l(x_1(l),\dots,x_n(l))$, while respecting the privacy of each user. For many functions $f_l$, data from the users are not all equally important, and there is potential to use the privacy budgets of the users strategically, leading to privacy savings that can be used to improve the utility of later queries. In particular, the budgeting should be adaptive to the outputs of previous queries, so that greater savings can be achieved on more typical instances. In this paper, we provide such an adaptive budgeting framework, with various applications demonstrating its applicability.

Figures (9)

• Figure 1: Relationships among different components of our framework.
• Figure 2: Selection of points to $G_{j}$ in the call $\mathrm{PIE}$-$\mathrm{NI}$ of Algorithm \ref{['algo:rc_pie_pm']} for range counting via point privatization. True locations: black solid dots; privatized locations: blue patterned dots. Solid green lines: points that advance to next round; gray dashed lines: points eliminated at this round. Assume $\bar{h}_{i,j}=\bar{h}_j$.
• Figure 3: Single query privacy savings: range counting for various $w$ and privacy parameter $\rho$.
• Figure 4: Single query privacy savings: KDE for various $b$ and privacy parameter $\rho$.
• Figure 5: Single query privacy savings: $k$NN for various $k$ and privacy parameter $\rho$.

Theorems & Definitions (49)

• Definition 1: Differential Privacy dwork2006calibrating
• Definition 2: Geo-Privacy chatzikokolakis2013broadeningliang2023concentrated
• Definition 3: Rényi Divergences renyi1961measuresvan2014renyi
• Definition 4: Concentrated Geo-Privacy liang2023concentrated
• Lemma 3.1: liang2023concentrated
• Lemma 3.2: liang2023concentrated
• Lemma 3.3: andres2013geoliang2023concentrated
• Lemma 3.4: Basic Mechanisms chatzikokolakis2013broadeningliang2023concentrated
• Theorem 4.1
• Theorem 4.2