Computing Maximal Per-Record Leakage and Leakage-Distortion Functions for Privacy Mechanisms under Entropy-Constrained Adversaries

Abstract: 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.