English(EN) Tight Lower Bounds under Matched High-Order H\"older Smoothness and Uniform Convexity

高阶凸优化的新理论界限已确立

作者 PulseAugur 编辑部 · [1 个来源] · 2026-11-05 05:00

研究人员在函数同时具有高阶Hölder光滑性和一致凸性且这些性质匹配的情况下，确立了优化的紧下界。该研究引用了Yuriy Nesterov的工作，为理解此类优化问题的复杂性提供了新的理论框架。这项工作解决了不对称情况下的下界悬而未决的问题，并为现有一阶界限提供了高阶一致凸的对应。 AI

影响为机器学习中使用的优化算法提供了理论基础。

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arXiv cs.LG TIER_1 English(EN) · Cedar Site Bai · 2026-11-05 05:00

匹配高阶 Hölder 光滑性和一致凸性下的严格下界

arXiv:2611.05527v1 Announce Type: cross Abstract: In this paper, we provide tight lower bounds for minimizing high-order H\"older-smooth and uniformly convex functions when their orders match. Specifically, we consider functions whose $p^{th}$-order derivatives are H\"older conti…