September 27, 2025Open Access
Revisiting Randomized Smoothing: Nonsmooth Nonconvex Optimization Beyond Global Lipschitz Continuity
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Implication
This study introduces a new subgradient growth condition for randomized smoothing, improving sample complexity for locally Lipschitz functions.
Key Points
- Randomized smoothing enhances optimization of nonsmooth functions, proving effective under relaxed conditions.
- The improved sample complexity is $ ilde{ ext{O}}(d^{3/2}δ^{-1}ε^{-3})$, aligning with optimal bounds for global Lipschitz functions.
- Novel algorithms based on generalized smoothness properties lead to convergence of $(δ, ε)$-Goldstein stationary points.
- Experimental validation reinforces the practicality and effectiveness of the proposed randomized smoothing algorithms.
Cite This Study
Xia et al. (2025) studied this question.