Improved Differential Privacy for SGD via Optimal Private Linear Operators on Adaptive Streams
This work addresses the need for enhanced privacy guarantees in federated learning, though it appears incremental as it builds on existing matrix mechanism frameworks.
The paper tackles the problem of achieving optimal differential privacy for SGD on adaptive streams by developing a parameter-free algorithm for computing optimal matrix factorizations, and demonstrates significant improvements in federated learning with user-level differential privacy.
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.