We investigate the rate-distortion-leakage region of the Chief Executive Officer (CEO) problem with a passive eavesdropper and privacy constraints, considering a general distortion measure. While an inner bound directly follows from the previous work, an outer bound is newly developed in this paper. To derive this bound, we introduce a new lemma tailored for analyzing privacy constraints. As a specific instance, we demonstrate that the tight bound for discrete and Gaussian sources is obtained when the eavesdropper can only observe the messages under logarithmic loss distortion. We further investigate the rate-distortion-leakage region for a scenario where the eavesdropper possesses the messages and side information under the same distortion, and provide an outer bound for this particular case. The derived outer bound differs from the inner bound by only a minor quantity that appears in the constraints associated with the privacy-leakage rates, and it becomes tight when the distortion is large.

翻译：我们研究了具有被动窃听者和隐私约束的首席执行官(CEO)问题的率-失真-泄露区域，考虑了一般失真度量。尽管内部界可直接从前人工作中得出，但本文新构建了一个外部界。为推导该界，我们引入了一个专门用于分析隐私约束的新引理。作为具体实例，我们证明当窃听者仅能在对数损失失真下观测消息时，离散源和高斯源的紧致界可被获得。我们进一步研究了在相同失真下窃听者拥有消息和边信息场景的率-失真-泄露区域，并给出了该特定情况的外部界。推导出的外部界仅在隐私泄露率相关约束中出现一个微小量而与内部界不同，且当失真较大时成为紧致界。