Gaussian Differential Privacy

Abstract In the past decade, differential privacy has seen remarkable success as a rigorous and practical formalization of data privacy. This definition its divergence based relaxations, however, have several acknowledged weaknesses, either in handling composition private algorithms or analysing important primitives like amplification by subsampling. Inspired hypothesis testing formulation privacy, this paper proposes new relaxation which we term ‘f-differential privacy’ (f-DP). notion number appealing properties and, particular, avoids difficulties associated with relaxations. First, f-DP faithfully preserves interpretation thereby making guarantees easily interpretable. addition, allows for lossless reasoning about an algebraic fashion. Moreover, provide powerful technique to import existing results proven original application technique, obtain simple easy-to-interpret theorem subsampling f-DP. addition above findings, introduce canonical single-parameter family notions within class that is referred ‘Gaussian (GDP), defined on two shifted Gaussian distributions. GDP focal among due central limit prove. More precisely, any (including definition) converges under composition. We also prove Berry–Esseen style version theorem, gives computationally inexpensive tool tractably exact algorithms. Taken together, collection attractive render mathematically coherent, analytically tractable versatile framework analysis. Finally, demonstrate use tools develop giving improved analysis noisy stochastic gradient descent.