Auditing Differential Privacy in the Black-Box Setting

Abstract: This paper introduces a novel theoretical framework for auditing differential privacy (DP) in a black-box setting. Leveraging the concept of $f$-differential privacy, we explicitly define type I and type II errors and propose an auditing mechanism based on conformal inference. Our approach robustly controls the type I error rate under minimal assumptions. Furthermore, we establish a fundamental impossibility result, demonstrating the inherent difficulty of simultaneously controlling both type I and type II errors without additional assumptions. Nevertheless, under a monotone likelihood ratio (MLR) assumption, our auditing mechanism effectively controls both errors. We also extend our method to construct valid confidence bands for the trade-off function in the finite-sample regime.