Motivated by recent applications requiring differential privacy over 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 adaptive streams, and provide a parameter-free fixed-point algorithm for computing optimal factorizations. We instantiate this framework with respect to concrete matrices which arise naturally in machine learning, and train user-level differentially private models with the resulting optimal mechanisms, yielding significant improvements in a notable problem in federated learning with user-level differential privacy.

翻译：基于最近要求适应性流有差异隐私的应用程序,我们调查了在这一背景下矩阵机制的最佳即时问题,证明了矩阵因子化适用于适应性流的基本理论结果,并为计算最佳因子化提供了一种无参数固定点算法。 我们对机器学习中自然产生的具体矩阵进行了这个框架的即时反应,并对用户一级差异性私人模型及其最佳机制进行了培训,从而在用户一级差异性隐私混合学习这一突出问题上取得了显著的改进。