针对有限对手的隐私-效用权衡
Privacy-Utility Trade-Offs Against Limited Adversaries
摘要：
我们研究的隐私效用权衡，用户与服务提供商分享隐私相关的有用信息，以获得一些实用程序。服务提供商是对抗性的，因为它可以根据共享的有用信息推断用户的隐私信息。为了最大限度地减少隐私泄漏，同时保持所需的效用水平，用户仔细扰动有用的信息，通过概率隐私映射之前sharingit. We专注于设置中的对手试图推断攻击用户的隐私有潜在的偏见的信息之间的统计相关性的私人和有用的变量。在相同的效用要求下，用户和有限对手之间的这种信息不对称导致比全知对手的情况下更好的隐私保证。我们首先确定对对手信息的假设，以便推理成本是明确且有限的。然后，我们描述了信息不对称的影响，并表明它增加了对手的推理成本。我们进一步制定的隐私映射的设计，对有限的对手使用凸函数的差异计划，并通过凹凸过程解决它。当对手的信息是不准确的，我们采用贝叶斯的观点，并表示对手的信息的概率分布。在这种情况下，对手的预期成本不允许一个封闭的形式的表达，我们建立和最大化的预期成本的下限。我们提供了一个关于人口普查数据集的数值例子来说明理论结果。
英文摘要：
We study privacy-utility trade-offs where users share privacy-correlated useful information with a service provider to obtain some utility. The service provider is adversarial in the sense that it can infer the users' private information based on the shared useful information. To minimize the privacy leakage while maintaining a desired level of utility, the users carefully perturb the useful information via a probabilistic privacy mapping before sharing it. We focus on the setting in which the adversary attempting an inference attack on the users' privacy has potentially biased information about the statistical correlation between the private and useful variables. This information asymmetry between the users and the limited adversary leads to better privacy guarantees than the case of the omniscient adversary under the same utility requirement. We first identify assumptions on the adversary's information so that the inference costs are well-defined and finite. Then, we characterize the impact of the information asymmetry and show that it increases the inference costs for the adversary. We further formulate the design of the privacy mapping against a limited adversary using a difference of convex functions program and solve it via the concave-convex procedure. When the adversary's information is not precisely available, we adopt a Bayesian view and represent the adversary's information by a probability distribution. In this case, the expected cost for the adversary does not admit a closed-form expression, and we establish and maximize a lower bound of the expected cost. We provide a numerical example regarding a census data set to illustrate the theoretical results.
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