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.

翻译：研究了同时满足两个差分隐私（DP）约束的机制的确切组合问题。由此产生的隐私区域可以精确表示为异构DP保证机制上组合的混合形式，从而形成一种自然推广到满足任意数量DP约束的机制组合的框架。这一结果通过二元假设检验混合的结构引理得以证明。最后，将所发展的方法应用于近似$f$-DP组合问题。