The Bounded Laplace Mechanism in Differential Privacy

TL;DR

This paper examines the limitations of the Laplace mechanism in differential privacy when bounding its support and introduces a robust method to optimize parameters to maintain privacy guarantees.

Contribution

It demonstrates that support bounding with standard parameters often breaks differential privacy and proposes a new method to compute optimal parameters for privacy preservation.

Findings

Bounding support without adjusting parameters can violate privacy

A new robust method for parameter optimization ensures differential privacy

The approach improves privacy guarantees in practical applications

Abstract

The Laplace mechanism is the workhorse of differential privacy, applied to many instances where numerical data is processed. However, the Laplace mechanism can return semantically impossible values, such as negative counts, due to its infinite support. There are two popular solutions to this: (i) bounding/capping the output values and (ii) bounding the mechanism support. In this paper, we show that bounding the mechanism support, while using the parameters of the pure Laplace mechanism, does not typically preserve differential privacy. We also present a robust method to compute the optimal mechanism parameters to achieve differential privacy in such a setting.