Efficient Private SCO for Heavy-Tailed Data via Averaged Clipping

• URL: http://arxiv.org/abs/2206.13011v4
• Date: Tue, 10 Sep 2024 04:11:27 GMT
• Title: Efficient Private SCO for Heavy-Tailed Data via Averaged Clipping
• Authors: Chenhan Jin, Kaiwen Zhou, Bo Han, James Cheng, Tieyong Zeng,
• Abstract summary: We consider differentially private convex optimization for heavy-tailed data with the guarantee of being differentially private (DP) We establish new convergence results and improved complexity bounds for the proposed algorithm called AClipped-dpSGD for constrained and unconstrained convex problems.
• Score: 40.69950711262191
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider stochastic convex optimization for heavy-tailed data with the guarantee of being differentially private (DP). Most prior works on differentially private stochastic convex optimization for heavy-tailed data are either restricted to gradient descent (GD) or performed multi-times clipping on stochastic gradient descent (SGD), which is inefficient for large-scale problems. In this paper, we consider a one-time clipping strategy and provide principled analyses of its bias and private mean estimation. We establish new convergence results and improved complexity bounds for the proposed algorithm called AClipped-dpSGD for constrained and unconstrained convex problems. We also extend our convergent analysis to the strongly convex case and non-smooth case (which works for generalized smooth objectives with H$\ddot{\text{o}}$lder-continuous gradients). All the above results are guaranteed with a high probability for heavy-tailed data. Numerical experiments are conducted to justify the theoretical improvement.

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