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Lower Bounds for Smooth Nonconvex Zeroth-Order Optimization: The Price of Determinism under Low Curvature Trace
Low curvature trace, an effective rank condition, is a common explanation for why randomized zeroth-order methods scale to high-dimensional tasks such as language model fine-tuning. Can deterministic methods achieve the same savings? We show that they cannot. We study finding $\varepsilon$-stationar
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