论文标题
多用户隐私机制设计，具有非零泄漏
Multi-User Privacy Mechanism Design with Non-zero Leakage
论文作者
论文摘要
通过信息理论的角度研究了隐私机制设计问题。在这项工作中，代理观察有用的数据$ y =（y_1，...，...，y_n）$，与私人数据$ x =（x_1，...，x_n）$相关，该$也可以被代理商访问。在这里，我们考虑了$ k $用户，其中用户$ i $需要$ y $的子向量，由$ c_ {i} $表示。代理商希望向用户$ i $披露$ c_ {i} $。由于$ c_ {i} $与$ x $相关，因此无法直接披露。隐私机制旨在生成公开的数据$ U $，该数据$ u $最大化用户实用程序的线性组合，同时满足相互信息的有限隐私约束。在类似的工作中，人们认为$ x_i $是$ y_i $的确定性函数，但是在这项工作中，我们让$ x_i $和$ y_i $是任意关联的。首先，通过使用特定的转换，功能表示引理和强大的功能代表引理来获得隐私 - 实用性权衡的上限，然后我们表明上限可以分解为$ n $并行问题。接下来，使用功能表示引理和强功能代表引理得出了隐私 - 实用性权衡方面的下限。上限在常数内紧密，并且下限断言，公开的数据独立于所有$ \ {x_j \} _ {i = 1}^n $，除了我们将最大允许泄漏分配给它。最后，在特殊情况下研究了所获得的边界。
A privacy mechanism design problem is studied through the lens of information theory. In this work, an agent observes useful data $Y=(Y_1,...,Y_N)$ that is correlated with private data $X=(X_1,...,X_N)$ which is assumed to be also accessible by the agent. Here, we consider $K$ users where user $i$ demands a sub-vector of $Y$, denoted by $C_{i}$. The agent wishes to disclose $C_{i}$ to user $i$. Since $C_{i}$ is correlated with $X$ it can not be disclosed directly. A privacy mechanism is designed to generate disclosed data $U$ which maximizes a linear combinations of the users utilities while satisfying a bounded privacy constraint in terms of mutual information. In a similar work it has been assumed that $X_i$ is a deterministic function of $Y_i$, however in this work we let $X_i$ and $Y_i$ be arbitrarily correlated. First, an upper bound on the privacy-utility trade-off is obtained by using a specific transformation, Functional Representation Lemma and Strong Functional Representaion Lemma, then we show that the upper bound can be decomposed into $N$ parallel problems. Next, lower bounds on privacy-utility trade-off are derived using Functional Representation Lemma and Strong Functional Representaion Lemma. The upper bound is tight within a constant and the lower bounds assert that the disclosed data is independent of all $\{X_j\}_{i=1}^N$ except one which we allocate the maximum allowed leakage to it. Finally, the obtained bounds are studied in special cases.
