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Yu-Xing Peng

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Preprint Aug 2026

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

It is proved the matching lower bound $\Omega(n+\sqrt n\,\Delta L_{\max}/\varepsilon^2)$ for randomized IFO algorithms, including those that choose component indices and query points from the full preceding history, and PAGE and SPIDER are minimax optimal up to universal constants under individual and mean-squared smoo...

Yu-Xing Peng, Zhi-Qing Tang, Wei-Jia Jia · 1 citation

#machine learning Preprint Aug 2026

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

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 prior lower bounds miss a factor of $\sqrt{n}$. We prove the matching lower bound for randomiz...

Yu-Xing Peng, Zhiqing Tang, Wei-Jia Jia · 0 citations