How can individuals exchange information to learn from each other despite their privacy needs and security concerns? For example, consider individuals deliberating a contentious topic and being concerned about divulging their private experiences. Preserving individual privacy and enabling efficient social learning are both important desiderata but seem fundamentally at odds with each other and very hard to reconcile. We do so by controlling information leakage using rigorous statistical guarantees that are based on differential privacy (DP). Our agents use log-linear rules to update their beliefs after communicating with their neighbors. Adding DP randomization noise to beliefs provides communicating agents with plausible deniability with regard to their private information and their network neighborhoods. We consider two learning environments one for distributed maximum-likelihood estimation given a finite number of private signals and another for online learning from an infinite, intermittent signal stream. Noisy information aggregation in the finite case leads to interesting tradeoffs between rejecting low-quality states and making sure all high-quality states are accepted in the algorithm output. Our results flesh out the nature of the trade-offs in both cases between the quality of the group decision outcomes, learning accuracy, communication cost, and the level of privacy protections that the agents are afforded.

翻译：个体如何在保护隐私和安全需求的前提下通过信息交换实现相互学习？例如，考虑一群人就争议性议题进行讨论，同时担忧泄露个人经历。保护个体隐私与促进高效社会学习虽同为重要目标，但本质矛盾且难以调和。本文通过基于差分隐私的严格统计保证来控制信息泄露，从而实现了二者的平衡。我们采用对数线性规则，使主体在与邻居通信后更新信念。在信念中添加差分隐私随机噪声，为通信主体提供了对其隐私信息及网络邻域的可否认性。我们研究了两种学习环境：基于有限数量私有信号的分布式最大似然估计，以及基于无限间歇信号流的在线学习。在有限信号情境下，噪声信息聚合会导致算法输出中在拒绝低质量状态与接受所有高质量状态之间产生有趣的权衡。我们的研究结果揭示了两种情境下群体决策结果质量、学习精度、通信成本与主体隐私保护水平间的权衡本质。