Composition Theorems for Multiple Differential Privacy Constraints
Cemre Cadir, Salim Najib, Yanina Y. Shkel
TL;DR
This paper develops a framework for understanding the exact composition of mechanisms under multiple differential privacy constraints, generalizing to multiple DP guarantees and applying to approximate f-DP composition.
Contribution
It introduces a structural lemma for mixtures of binary hypothesis tests to characterize the privacy region under multiple DP constraints.
Findings
Exact representation of the privacy region as a mixture over heterogeneous DP mechanisms
Generalization to composition of mechanisms with any number of DP constraints
Application to approximate f-DP composition
Abstract
The exact composition of mechanisms for which two differential privacy (DP) constraints hold simultaneously is studied. The resulting privacy region admits an exact representation as a mixture over compositions of mechanisms of heterogeneous DP guarantees, yielding a framework that naturally generalizes to the composition of mechanisms for which any number of DP constraints hold. This result is shown through a structural lemma for mixtures of binary hypothesis tests. Lastly, the developed methodology is applied to approximate -DP composition.
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