2014/07/07 by Jonathan Ullman, Ullman, Jonathan · 1 citation
Computer Science · #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Privacy-Preserving Technologies in Data #Stochastic Gradient Optimization Techniques #cs.DS
paper · pdf · doi:10.48550/arxiv.1407.1571
openalex publication_date 2014/07/07 · arxiv created 2015/03/14 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A wide variety of fundamental data analyses in machine learning, such as linear and logistic regression, require minimizing a convex function defined by the data. Since the data may contain sensitive information about individuals, and these analyses can leak that sensitive information, it is important to be able to solve convex minimization in a privacy-preserving way. A series of recent results show how to accurately solve a single convex minimization problem in a differentially private manner. However, the same data is often analyzed repeatedly, and little is known about solving multiple convex minimization problems with differential privacy. For simpler data analyses, such as linear queries, there are remarkable differentially private algorithms such as the private multiplicative weights mechanism (Hardt and Rothblum, FOCS 2010) that accurately answer exponentially many distinct queries. In this work, we extend these results to the case of convex minimization and show how to give accurate and differentially private solutions to *exponentially many* convex minimization problems on a sensitive dataset.