Learning with User-Level Privacy

Abstract

We propose and analyze algorithms to solve a range of learning tasks under user-level differential privacy constraints. Rather than guaranteeing only the privacy of individual samples, user-level DP protects a user's entire contribution ($m\ge 1$ samples), providing more stringent but more realistic protection against information leaks. We show that for high-dimensional mean estimation, empirical risk minimization with smooth losses, stochastic convex optimization, and learning hypothesis classes with finite metric entropy, the privacy cost decreases as $O(1/\sqrt{m})$ as users provide more samples. In contrast, when increasing the number of users $n$, the privacy cost decreases at a faster $O(1/n)$ rate. We complement these results with lower bounds showing the minimax optimality of our algorithms for mean estimation and stochastic convex optimization. Our algorithms rely on novel techniques for private mean estimation in arbitrary dimension with error scaling as the concentration radius $\tau$ of the distribution rather than the entire range.

arXiv commentNeurIPS 2021. 43 pages, 0 figure

References in corpus (8)

• Learning Differentially Private Recurrent Language Models
• Distributed Mean Estimation with Limited Communication
• Private Stochastic Convex Optimization with Optimal Rates
• A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm
• Privacy and Statistical Risk: Formalisms and Minimax Bounds
• The Cost of Privacy: Rates of Convergence for Parameter Estimation with Differential Privacy
• Private Mean Estimation of Heavy-Tailed Distributions
• Learning discrete distributions: user vs item-level privacy

Cited by in corpus (1)

• Adapting to Function Difficulty and Growth Conditions in Private Optimization