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性质。由此产生的隐私区域可精确表示为由异质DP保证的机制组合上的混合分布，这一框架自然推广至满足任意数量DP约束的机制组合。该结果通过关于二元假设检验混合的结构引理得以证明。最后，将所发展的方法论应用于近似$f$-DP的组合分析。