# Two Views of Constrained Differential Privacy: Belief Revision and Update

## TL;DR

This paper presents two conceptual frameworks for constrained differential privacy—belief revision and belief update—using probabilistic conditioning and optimization, respectively, to analyze properties and utility of DP mechanisms.

## Contribution

It introduces two perspectives for constrained DP, connecting belief revision and update, and applies these to analyze properties and utility of existing mechanisms.

## Key findings

- Constrained DP can be viewed as belief revision or update.
- New composition properties for constrained DP are established.
- Differences in utility between the two views are demonstrated.

## Abstract

In this paper, we provide two views of constrained differential private (DP) mechanisms. The first one is as belief revision. A constrained DP mechanism is obtained by standard probabilistic conditioning, and hence can be naturally implemented by Monte Carlo algorithms. The other is as belief update. A constrained DP is defined according to l2-distance minimization postprocessing or projection and hence can be naturally implemented by optimization algorithms. The main advantage of these two perspectives is that we can make full use of the machinery of belief revision and update to show basic properties for constrained differential privacy especially some important new composition properties. Within the framework established in this paper, constrained DP algorithms in the literature can be classified either as belief revision or belief update. At the end of the paper, we demonstrate their differences especially in utility in a couple of scenarios.