We investigate the rate-distortion-leakage region of the Chief Executive Officer (CEO) problem, considering the presence of a passive eavesdropper and privacy constraints. We start by examining the region where a general distortion measure quantifies the distortion. While the inner bound of the region is derived from previous work, this paper newly develops an outer bound. To derive the outer bound, we introduce a new lemma tailored for analyzing privacy constraints. Next, as a specific instance of the general distortion measure, we demonstrate that the tight bound for discrete and Gaussian sources is obtained when the eavesdropper has no side information, and the distortion is quantified by the log-loss distortion measure. We further investigate the rate-distortion-leakage region for a scenario where the eavesdropper has side information, and the distortion is quantified by the log-loss distortion measure and provide an outer bound for this 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 these bounds match when the distortion is large.

翻译：本研究探讨了存在被动窃听者与隐私约束条件下，首席执行官（CEO）问题的率失真泄露区域。我们首先考察了采用一般失真度量量化失真的区域。虽然该区域的内边界可从已有研究中导出，但本文创新性地推导了其外边界。为获得此外边界，我们引入了一个专门用于分析隐私约束的新引理。随后，作为一般失真度量的特例，我们证明了当窃听者无侧信息且失真采用对数损失度量时，离散与高斯信源的紧致边界是可获得的。我们进一步研究了窃听者具备侧信息且失真采用对数损失度量时的率失真泄露区域，并给出了该情形下的外边界。推导所得外边界与内边界仅在隐私泄露率相关约束项上存在微小差异，且当失真较大时，二者完全吻合。