【论文记录】Renyi Differential Privacy

【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

• ε varepsilon ε-differential privacy的(利用Max Divergence)等价定义 :
  quad A randomized mechanism f f f is ε varepsilon ε-differentially private if and only if its distribution over any two adjacent inputs D D D and D ′ D' D′ satisfies : D ∞ ( f ( D ) ∥ f ( D ′ ) ) ≤ ε ,, D_infty big( f(D) | f(D') big) le varepsilon D∞​(f(D)∥f(D′))≤ε
  quad 注: 此种等价定义在《The Algorithmic Foundations of Differential Privacy》一书中也有提及，详见 P 44 mathcal P_{mathcal{44}} P44​

• 在此基础上进行拓展,(利用Renyi Divergence)得到Renyi differential privacy :
  quad A randomized mechanism f f f: D ↦ R mathcal D mapsto mathcal R D↦R is said to have ε varepsilon ε-Renyi differential privacy of order α alpha α, or ( α alpha α, ε varepsilon ε)-RDP for short, if for any adjacent D D D, D ′ D' D′ ∈ D in mathcal D ∈D it holds that : D α ( f ( D ) ∥ f ( D ′ ) ) ≤ ε ,, D_alpha big( f(D) | f(D') big) le varepsilon Dα​(f(D)∥f(D′))≤ε
  quad 注: Renyi Divergence的定义中令 α alpha α趋于无穷即得到 Max Divergence

• Renyi differential privacy 满足的 ε varepsilon ε-differential privacy的一些性质

IV. RDP AND ( ε varepsilon ε, δ delta δ)-DP

• Renyi differential privacy 的定义也满足 ( ε ′ varepsilon' ε′, δ ′ delta' δ′)-differential privacy 的定义

Ref

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