Improved Differential Privacy for SGD via Optimal Private Linear Operators on Adaptive Streams

Serguei Denissov, Hugh Brendan McMahan, J Keith Rush, Adam Smith, Abhradeep Guha Thakurta

Keywords: federated learning, differential privacy, adaptive streams, machine learning, matrix mechanism, matrix factorization

TL;DR: We provide new insights into optimizing differential privacy queries under adaptive streams, generalize from the study of the prefix-sum query, and demonstrate that these optimized mechanisms can significantly improve performance.

Abstract: Motivated by recent applications requiring differential privacy in the setting of adaptive streams, we investigate the question of optimal instantiations of the matrix mechanism in this setting. We prove fundamental theoretical results on the applicability of matrix factorizations to the adaptive streaming setting, and provide a new parameter-free fixed-point algorithm for computing optimal factorizations. We instantiate this framework with respect to concrete matrices which arise naturally in the machine learning setting, and train user-level differentially private models with the resulting optimal mechanisms, yielding significant improvements on a notable problem in federated learning with user-level differential privacy.