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Fast Optimal Locally Private Mean Estimation via Random Projections
Hilal Asi · Vitaly Feldman · Jelani Nelson · Huy Nguyen · Kunal Talwar

Wed Dec 13 08:45 AM -- 10:45 AM (PST) @ Great Hall & Hall B1+B2 #1907
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, namely 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 and then runs an optimal algorithm such a PrivUnitG in the lower dimensional space. We analyze the error of the algorithm in terms of properties of the random projection ensemble, and study two instantiations. We conduct several experiments for private mean estimation and private federated learning which demonstrate that our algorithms obtain nearly the same utility as optimal algorithms while having significantly lower communication and computational cost.

Author Information

Hilal Asi (Apple)
Vitaly Feldman (Apple)
Jelani Nelson (UC Berkeley)

Jelani Nelson is a Professor of Electrical Engineering and Computer Sciences at UC Berkeley, and also a Research Scientist at Google (part-time). He is interested in randomized algorithms, sketching and streaming algorithms, dimensionality reduction, and differential privacy. He is a recipient of the ACM Eugene L. Lawler Award for Humanitarian Contributions within Computer Science, a Presidential Early Career Award for Scientist and Engineers (PECASE), and a Sloan Research Fellowship. He is also Founder and President of AddisCoder, Inc., a nonprofit that provides algorithms training to high school students in Ethiopia and Jamaica.

Huy Nguyen (Northeastern University)
Kunal Talwar (Apple)

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