🤖 AI Summary
This work addresses the challenge of precisely characterizing the overall privacy guarantee when composing mechanisms under multiple heterogeneous differential privacy (DP) constraints. The authors propose a general composition framework that, for the first time, enables an exact description of the resulting privacy region after composing an arbitrary number of mechanisms subject to diverse DP bounds. By constructing a binary hypothesis testing–based mixture model and integrating probabilistic mixing with f-DP approximation techniques, the framework yields an exact composition theorem for multiple DP constraints. Moreover, the approach naturally extends to the f-DP setting, significantly enhancing both the tightness and applicability of compositional privacy analysis.
📝 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 $f$-DP composition.