2023/06/07 by Hilal Asi, Vitaly Feldman, Asi, Hilal +7 · 2 citations
Computer Science · Mathematics · #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Privacy-Preserving Technologies in Data #Random Matrices and Applications #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2306.04444
openalex publication_date 2023/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem of locally private mean estimation of high-dimensional vectors in the Euclidean ball. Existing algorithms for this problem either incur sub-optimal error or have high communication and/or run-time complexity. We propose a new algorithmic framework, ProjUnit, for private mean estimation that yields algorithms that are computationally efficient, have low communication complexity, and incur optimal error up to a 1+o(1)-factor. Our framework is deceptively simple: each randomizer projects its input to a random low-dimensional subspace, normalizes the result, and then runs an optimal algorithm such as PrivUnitG in the lower-dimensional space. In addition, we show that, by appropriately correlating the random projection matrices across devices, we can achieve fast server run-time. We mathematically analyze the error of the algorithm in terms of properties of the random projections, and study two instantiations. Lastly, our experiments for private mean estimation and private federated learning demonstrate that our algorithms empirically obtain nearly the same utility as optimal ones while having significantly lower communication and computational cost.