Two Views of Constrained Differential Privacy: Belief Revision and Update
This work offers a theoretical framework for classifying and analyzing constrained DP algorithms, which is incremental as it builds on existing literature without introducing new methods.
The paper tackles the problem of understanding constrained differential privacy mechanisms by providing two perspectives: belief revision via probabilistic conditioning and belief update via l2-distance minimization, and it demonstrates their differences in utility across scenarios.
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.