The exponential growth of data collection necessitates robust privacy protections that preserve data utility. We address information disclosure against adversaries with bounded prior knowledge, modeled by an entropy constraint $H(X) \geq b$. Within this information privacy framework -- which replaces differential privacy's independence assumption with a bounded-knowledge model -- we study three core problems: maximal per-record leakage, the primal leakage-distortion tradeoff (minimizing worst-case leakage under distortion $D$), and the dual distortion minimization (minimizing distortion under leakage constraint $L$). These problems resemble classical information-theoretic ones (channel capacity, rate-distortion) but are more complex due to high dimensionality and the entropy constraint. We develop efficient alternating optimization algorithms that exploit convexity-concavity duality, with theoretical guarantees including local convergence for the primal problem and convergence to a stationary point for the dual. Experiments on binary symmetric channels and modular sum queries validate the algorithms, showing improved privacy-utility tradeoffs over classical differential privacy mechanisms. This work provides a computational framework for auditing privacy risks and designing certified mechanisms under realistic adversary assumptions.

翻译：数据收集的指数级增长亟需在保持数据效用的前提下提供鲁棒的隐私保护。本文针对具有有限先验知识的对手（通过熵约束$H(X) \geq b$建模）下的信息泄露问题展开研究。在此信息隐私框架（该框架以有限知识模型替代差分隐私的独立性假设）中，我们探讨三个核心问题：最大单记录泄漏、原始泄漏-失真权衡（在失真度$D$约束下最小化最坏情况泄漏）以及对偶失真最小化（在泄漏约束$L$下最小化失真）。这些问题类似于经典信息论问题（信道容量、率失真理论），但因高维特性与熵约束而更为复杂。我们开发了利用凸凹对偶性的高效交替优化算法，并给出理论保证：原始问题具有局部收敛性，对偶问题收敛至稳定点。在二元对称信道与模和查询上的实验验证了算法有效性，其隐私-效用权衡优于经典差分隐私机制。本研究为实际对手假设下的隐私风险审计与认证机制设计提供了计算框架。