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Corpus ID: 232092592

Private Stochastic Convex Optimization: Optimal Rates in 𝓁1 Geometry

@article{Asi2021PrivateSC,
title={Private Stochastic Convex Optimization: Optimal Rates in 𝓁1 Geometry},
author={Hilal Asi and V. Feldman and T. Koren and Kunal Talwar},
journal={ArXiv},
year={2021},
volume={abs/2103.01516}
}

Stochastic convex optimization over an l1-bounded domain is ubiquitous in machine learning applications such as LASSO but remains poorly understood when learning with differential privacy. We show that, up to logarithmic factors the optimal excess population loss of any (ε, δ)-differentially private optimizer is √ log(d)/n + √ d/εn. The upper bound is based on a new algorithm that combines the iterative localization approach of Feldman et al. [FKT20] with a new analysis of private regularized… Expand