The Privacy-Utility Tradeoff of Robust Local Differential Privacy

TL;DR

This paper introduces the Robust Local Differential Privacy (RLDP) framework that provides privacy guarantees considering data distribution uncertainties, proposing optimal and practical algorithms that improve data utility over standard LDP.

Contribution

The paper develops the RLDP framework, introduces an optimal protocol for the worst-case distribution, and proposes four algorithms, including low-complexity methods based on randomized response.

Findings

The optimal protocol is effective in the low privacy regime.

Algorithms significantly improve utility compared to standard LDP.

Polytope-based method offers high utility but is computationally intensive.

Abstract

We consider data release protocols for data $X=(S,U)$, where $S$ is sensitive; the released data $Y$ contains as much information about $X$ as possible, measured as $\operatorname{I}(X;Y)$, without leaking too much about $S$. We introduce the Robust Local Differential Privacy (RLDP) framework to measure privacy. This framework relies on the underlying distribution of the data, which needs to be estimated from available data. Robust privacy guarantees are ensuring privacy for all distributions in a given set $\mathcal{F}$, for which we study two cases: when $\mathcal{F}$ is the set of all distributions, and when $\mathcal{F}$ is a confidence set arising from a $\chi^2$ test on a publicly available dataset. In the former case we introduce a new release protocol which we prove to be optimal in the low privacy regime. In the latter case we present four algorithms that construct RLDP protocols from a given dataset. One of these approximates $\mathcal{F}$ by a polytope and uses results from robust optimisation to yield high utility release protocols. However, this algorithm relies on vertex enumeration and becomes computationally inaccessible for large input spaces. The other three algorithms are low-complexity and build on randomised response. Experiments verify that all four algorithms offer significantly improved utility over regular LDP.