Year: 2024
Type: article
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 $$\ddot{\text {o}}$$ 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.
Source: Machine Learning
Institutions: Chinese University of Hong Kong, Hong Kong Baptist University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4402975049