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# Balancing utility and scalability in metric differential privacy

*Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence*, PMLR 180:885-894, 2022.

#### Abstract

Metric differential privacy (mDP) is a modification of differential privacy that is more suitable when records can be represented in a general metric space, such as text data represented as word embed- dings or geographical coordinates on a map. We consider the task of releasing elements of the metric space under metric differential privacy where utility is measured as the distance of the released element to the original element. Linear programming (LP) can be used to construct a mechanism that achieves the optimal utility for a particular mDP constraint. However, these LPs suffer from a polynomial explosion of variables and constraints that render them impractical for solving real-world problems. An important question is how to design rigorous mDP mechanisms that balance the utility- scalability tradeoff. Our main contribution is a new method for reducing the LP size used to generate mDP mechanisms by constraining the search space such that certain input and output pairs have transition probabilities derived from the exponential mechanism. Our method produces mDP mechanisms whose LPs are smaller that all prior work in this area. We also provide a lower bound on the best possible mechanism utility. Our experiments on real-world metric spaces highlight the superior utility-scalability tradeoff of our mechanism.