Outer Bounds on the CEO Problem with Privacy Constraints

2023-01-29

IEEE Transactions on Information Forensics and Security

AI Summary

This paper investigates the distributed estimation problem under privacy constraints—the “CEO problem with eavesdroppers”—aiming to characterize the feasible region of rate-distortion-leakage trade-offs. Methodologically, it introduces novel information-theoretic inequalities tailored for privacy analysis, applicable to both general distortion measures and log-loss distortion; these yield tight outer bounds on the achievable region. For log-loss distortion and in the absence of eavesdropper side information, the inner and outer bounds match exactly for both discrete and Gaussian sources. When the eavesdropper possesses side information, the outer and inner bounds differ only by a first-order term in the leakage rate and coincide precisely in the high-distortion regime. The work provides a unified framework for quantifying the fundamental trade-off between estimation accuracy and privacy preservation, establishing theoretical foundations and performance limits for privacy-sensitive distributed learning.

Abstract

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.

Problem

• Privacy-constrained CEO problem
• Information distortion
• Eavesdropper's knowledge

Innovation

• Privacy-Constrained CEO Problem
• Outer Bound Analysis
• Logarithmic Distortion Measure