A series of recent works by Lyu, Wang, Vadhan, and Zhang (TCC `21, NeurIPS `22, STOC `23) showed that composition theorems for non-interactive differentially private mechanisms extend to the concurrent composition of interactive differentially private mechanism, when differential privacy is measured using $f$-DP and the adversary is adaptive. We extend their work to the $\textit{continual observation setting,}$ where the data is arriving online in a potentially adaptive manner. More specifically, we show that all composition theorems for non-interactive differentially private mechanisms extend to the concurrent composition of continual differentially private mechanism, where the adversary is adaptive. We show this result for $f$-DP, which also implies the result for pure DP and $(\epsilon, \delta)$-DP.

翻译：Lyu、Wang、Vadhan 和 Zhang 近期的一系列工作（TCC `21, NeurIPS `22, STOC `23）表明，当使用 $f$-DP 衡量差分隐私且敌手具有自适应性时，非交互式差分隐私机制的组合定理可以扩展到交互式差分隐私机制的并发组合。我们将他们的工作推广到 $\textit{持续观测场景}$，其中数据以潜在的自适应方式在线到达。具体而言，我们证明了所有针对非交互式差分隐私机制的组合定理均可扩展到持续差分隐私机制的并发组合，且敌手具有自适应性。我们在 $f$-DP 框架下证明了该结果，该结果也意味着其对纯 DP 和 $(\epsilon, \delta)$-DP 的适用性。