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New Dense Weak Hiding framework closes optimization complexity gaps

By PulseAugur Editorial · [1 sources] ·

Researchers have developed a new theoretical framework called Dense Weak Hiding to address complexity gaps in nonconvex and Polyak-Lojasiewicz (PL) finite-sum optimization. This framework establishes matching lower bounds for randomized first-order oracle algorithms, determining the minimax IFO complexity under both individual and mean-squared smoothness conditions. The proposed method utilizes a fixed sign table to distribute hidden directions across components, ensuring each queried row provides minimal information while preserving the full signal in the row average. This approach is designed to handle arbitrary query points and make unopened links invisible to function values and gradients, ultimately achieving a missing $\sqrt{n}$ factor in complexity. AI

IMPACT This theoretical advancement could lead to more efficient optimization algorithms for machine learning models.

RANK_REASON The cluster contains a research paper detailing a new theoretical framework for 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 Dense Weak Hiding framework closes optimization complexity gaps

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The cluster contains a research paper detailing a new theoretical framework for 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) · Yuxing Peng, Zhiqing Tang, Weijia Jia ·

    Dense Weak Hiding: Closing Complexity Gaps in Nonconvex and PL Finite-Sum Optimization under Individual Smoothness

    arXiv:2609.00045v1 Announce Type: cross Abstract: Under individual smoothness, the optimal incremental first-order oracle (IFO) complexity of nonconvex finite-sum optimization has remained open. Known algorithms use $O(n+\sqrt{n}\,\Delta L_{\max}/\varepsilon^2)$ calls, while prio…

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