【论文记录】Renyi Differential Privacy

II. DIFFERENTIAL PRIVACY AND ITS FLAVORS

• 讨论各个差分隐私机制的优缺点

III. RENYI DIFFERENTIAL PRIVACY

• $\epsilon$-differential privacy的(利用Max Divergence)等价定义 :
  \quad A randomized mechanism $f$ is $\epsilon$-differentially private if and only if its distribution over any two adjacent inputs $D$ and $D^{\prime }$ satisfies : $D_{\infty }(f(D)\Vert f(D^{\prime }))\le \epsilon$
  \quad 注: 此种等价定义在《The Algorithmic Foundations of Differential Privacy》一书中也有提及，详见 ${\mathcal{P}}_{44}$

• 在此基础上进行拓展,(利用Renyi Divergence)得到Renyi differential privacy :
  \quad A randomized mechanism $f$: $\mathcal{D}\mapsto \mathcal{R}$ is said to have $\epsilon$-Renyi differential privacy of order $\alpha$, or ($\alpha$,$\epsilon$)-RDP for short, if for any adjacent $D$, $D^{\prime }$ $\in \mathcal{D}$ it holds that : $D_{\alpha }(f(D)\Vert f(D^{\prime }))\le \epsilon$
  \quad 注: Renyi Divergence的定义中令$\alpha$趋于无穷即得到 Max Divergence

• Renyi differential privacy 满足的$\epsilon$-differential privacy的一些性质

IV. RDP AND ($\epsilon$,$\delta$)-DP

• Renyi differential privacy 的定义也满足 (${\epsilon }^{\prime }$,${\delta }^{\prime }$)-differential privacy 的定义

Ref

I. Mironov. Renyi differential privacy. Private communication, 2016.