Document Type
Conference Proceeding
Publication Title
Proceedings of Machine Learning Research
Abstract
In this paper, we revisit the problem of Differentially Private Stochastic Convex Optimization (DP-SCO) in Euclidean and general `dp spaces. Specifically, we focus on three settings that are still far from well understood: (1) DP-SCO over a constrained and bounded (convex) set in Euclidean space; (2) unconstrained DP-SCO in `dp space; (3) DP-SCO with heavy-tailed data over a constrained and bounded set in `dp space. For problem (1), for both convex and strongly convex loss functions, we propose methods whose outputs could achieve (expected) excess population risks that are only dependent on the Gaussian width of the constraint set, rather than the dimension of the space. Moreover, we also show the bound for strongly convex functions is optimal up to a logarithmic factor. For problems (2) and (3), we propose several novel algorithms and provide the first theoretical results for both cases when 1 < p < 2 and 2 ≤ p ≤ ∞.
First Page
2026
Last Page
2035
Publication Date
1-1-2023
Keywords
Geometry, Stochastic systems
Recommended Citation
J. Su et al., "Differentially Private Stochastic Convex Optimization in (Non)-Euclidean Space Revisited," Proceedings of Machine Learning Research, vol. 216, pp. 2026 - 2035, Jan 2023.
Comments
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