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要求在不损害数据效用性的同时提供强大的隐私保护。我们针对具有有界先验知识的对手（由熵约束$H(X) \geq b$建模）的信息披露问题展开研究。在此信息隐私框架下——该框架用有界知识模型替代了差分隐私的独立性假设——我们研究了三个核心问题：最大每记录泄露、原始泄露-失真权衡（在失真$D$下最小化最坏情况泄露）以及对偶失真最小化（在泄露约束$L$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），但由于高维度和熵约束而更为复杂。我们开发了利用凸-凹对偶性的高效交替优化算法，具有理论保证，包括原始问题的局部收敛性以及对偶问题的驻点收敛性。在二进制对称信道和模数求和查询上的实验验证了该算法，显示出相比经典差分隐私机制在隐私-效用权衡上的改进。本研究为在现实对手假设下审计隐私风险并设计经认证机制提供了计算框架。