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New theoretical bounds for high-order convex optimization established

By PulseAugur Editorial · [1 sources] ·

Researchers have established tight lower bounds for optimizing functions that exhibit both high-order Hölder smoothness and uniform convexity, specifically when these properties match. The study, which references the work of Yuriy Nesterov, provides a new theoretical framework for understanding the complexity of such optimization problems. This work resolves an open question regarding lower bounds in asymmetric regimes and offers a higher-order uniformly convex counterpart to existing first-order bounds. AI

IMPACT Provides theoretical underpinnings for optimization algorithms used in machine learning.

RANK_REASON Academic paper detailing theoretical bounds in optimization. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

New theoretical bounds for high-order convex optimization established

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Academic paper detailing theoretical bounds in optimization. [lever_c_demoted from research: ic=1 ai=1.0]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Cedar Site Bai ·

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

    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…

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