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arXiv · 2404.10881

Differentially Private Optimization with Sparse Gradients

Badih Ghazi·Cristóbal Guzmán·Pritish Kamath·Ravi Kumar·Pasin Manurangsi
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Abstract

Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with sparse data, improving upon existing algorithms particularly for the high-dimensional regime. Building on this, we obtain pure- and approximate-DP algorithms with almost optimal rates for stochastic convex optimization with sparse gradients; the former represents the first nearly dimension-independent rates for this problem. Finally, we study the approximation of stationary points for the empirical loss in approximate-DP optimization and obtain rates that depend on sparsity instead of dimension, modulo polylogarithmic factors.

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Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Ravi Kumar, Pasin Manurangsi. 2024-04-16. Differentially Private Optimization with Sparse Gradients. https://arxiv.org/abs/2404.10881

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