As members of network systems share more information among agents and with network providers, sensitive data leakage raises privacy concerns. Motivated by such concerns, we introduce a novel mechanism that privatizes vectors belonging to the unit simplex. Such vectors can be found in many applications, such as privatizing a decision-making policy in a Markov decision process. We use differential privacy as the underlying mathematical framework for this work. The introduced mechanism is a probabilistic mapping that maps a vector within the unit simplex to the same domain using a Dirichlet distribution. We find the mechanism well-suited for inputs within the unit simplex because it always returns a privatized output that is also in the unit simplex. Therefore, no further projection back onto the unit simplex is required. We verify and quantify the privacy guarantees of the mechanism for three cases: identity queries, average queries, and general linear queries. We establish a trade-off between the level of privacy and the accuracy of the mechanism output, and we introduce a parameter to balance the trade-off between them. Numerical results illustrate the proposed mechanism.

中文翻译：

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通过狄利克雷机制实现单工单元上的差分隐私


随着网络系统成员在代理之间以及与网络提供商之间共享更多信息，敏感数据泄露引发了隐私问题。出于这种担忧，我们引入了一种新颖的机制，将属于单位单纯形的向量私有化。这种向量可以在许多应用中找到，例如马尔可夫决策过程中的决策策略私有化。我们使用差异隐私作为这项工作的基础数学框架。引入的机制是一种概率映射，它使用狄利克雷分布将单位单纯形内的向量映射到同一域。我们发现该机制非常适合单元单纯形内的输入，因为它总是返回也在单元单纯形内的私有化输出。因此，不需要进一步投影回到单位单纯形上。我们针对身份查询、平均查询和一般线性查询三种情况验证并量化了该机制的隐私保证。我们在隐私级别和机制输出的准确性之间建立权衡，并引入一个参数来平衡它们之间的权衡。数值结果说明了所提出的机制。