Differentially Private Optimization with Sparse Gradients

• URL: http://arxiv.org/abs/2404.10881v2
• Date: Thu, 31 Oct 2024 15:27:40 GMT
• Title: Differentially Private Optimization with Sparse Gradients
• Authors: Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Ravi Kumar, Pasin Manurangsi,
• Abstract summary: We study differentially private (DP) optimization problems under sparsity of individual gradients. Building on this, we obtain pure- and approximate-DP algorithms with almost optimal rates for convex optimization with sparse gradients.
• Score: 60.853074897282625
• License:
• 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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