差分隐私贝叶斯劝说
Differentially Private Bayesian Persuasion
AI总结：
本文研究差分隐私约束下的贝叶斯劝说问题，从后验发布和行动推荐两个视角刻画隐私对信息披露与发送方效用的影响，并给出最优信号方案的几何特征及多项式时间计算算法。
摘要：
劝说与隐私保护之间的张力在现实场景中普遍存在。在线平台在收集网络用户数据的同时，既要保护用户隐私，又要披露这些数据信息以出售广告位。类似地，医院可以在承担保护患者隐私义务的前提下共享患者数据以吸引研究投资。为了解决这些问题，我们构建了一个在差分隐私约束下研究贝叶斯劝说的框架，其中发送方必须设计最优的信号方案以实现劝说，同时保证数据库中每个智能体私有信息的隐私。为了理解隐私约束如何影响信息披露，我们在贝叶斯劝说中探索两种视角：一种将机制视为发布关于私有数据的后验，另一种将其视为发送行动推荐。基于后验的表述有助于考虑隐私与效用的权衡，量化隐私约束的严格程度如何影响发送方的最优效用。对于一个常见效用函数族中的任意实例以及广泛的隐私水平范围，在三种条件——ε-差分隐私约束、松弛的(ε,δ)-差分隐私约束和无隐私约束——中的任意两者之间，都可以发现显著的常数效用差距。我们进一步从几何上刻画了在不同类型约束（ε-差分隐私、(ε,δ)-差分隐私和Renyi差分隐私）下的最优信号方案，所有这些方案都可以视为在受限后验区域中寻找凹包。同时，通过采用基于行动的劝说视角，只要满足一个温和的齐次性条件，我们就提供了计算最优差分隐私信号方案的多项式时间算法。
英文摘要：
The tension between persuasion and privacy preservation is common in real-world settings. Online platforms should protect the privacy of web users whose data they collect, even as they seek to disclose information about these data to selling advertising spaces. Similarly, hospitals may share patient data to attract research investments with the obligation to preserve patients' privacy. To deal with these issues, we develop a framework to study Bayesian persuasion under differential privacy constraints, where the sender must design an optimal signaling scheme for persuasion while guaranteeing the privacy of each agent's private information in the database. To understand how privacy constraints affect information disclosure, we explore two perspectives within Bayesian persuasion: one views the mechanism as releasing a posterior about the private data, while the other views it as sending an action recommendation. The posterior-based formulation helps consider privacy-utility tradeoffs, quantifying how the tightness of privacy constraints impacts the sender's optimal utility. For any instance in a common utility function family and a wide range of privacy levels, a significant constant utility gap can be found between any two of the three conditions: $ε$-differential privacy constraint, relaxation $(ε,δ)$-differential privacy constraint, and no privacy constraint. We further geometrically characterize optimal signaling schemes under different types of constraints ($ε$-differential privacy, $(ε,δ)$-differential privacy and Renyi differential privacy), all of which can be seen as finding concave hulls in constrained posterior regions. Meanwhile, by taking the action-based view of persuasion, we provide polynomial-time algorithms for computing optimal differentially private signaling schemes, as long as a mild homogeneous condition is met.
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