In this paper we provide an algorithmic framework based on Langevin diffusion (LD) and its corresponding discretizations that allow us to simultaneously obtain: i) An algorithm for sampling from the exponential mechanism, whose privacy analysis does not depend on convexity and which can be stopped at anytime without compromising privacy, and ii) tight uniform stability guarantees for the exponential mechanism. As a direct consequence, we obtain optimal excess empirical and population risk guarantees for (strongly) convex losses under both pure and approximate differential privacy (DP). The framework allows us to design a DP uniform sampler from the Rashomon set. Rashomon sets are widely used in interpretable and robust machine learning, understanding variable importance, and characterizing fairness.

翻译：本文提出一种基于Langevin扩散（LD）及其离散化的算法框架，可同时实现以下目标：(i) 一种从指数机制中采样的算法，其隐私分析不依赖于凸性，且可在任意时刻终止而不损害隐私；(ii) 为指数机制提供严格的均匀稳定性保证。作为直接推论，我们在纯差分隐私（DP）和近似差分隐私下，针对（强）凸损失函数获得了最优的超额经验风险与总体风险保证。该框架使我们能够设计从Rashomon集中进行差分隐私均匀采样的方法。Rashomon集被广泛应用于可解释机器学习、鲁棒机器学习、变量重要性理解及公平性刻画等领域。