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Author

Kai-Zhao Liu

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#machine learning Preprint Sep 2026

Silver Rate Is (Almost) Optimal for Gradient Descent

We study how far gradient descent (GD) can be accelerated by predetermined stepsizes in smooth convex optimization. Writing $p_{\mathrm{sil}}=\log_2(1+\sqrt{2})$, we prove an $\Omega\left(n^{-p_{\mathrm{sil}}-O(\sqrt{\log\log n/\log n})}\right)$ non-anytime lower bound. In the anytime setting, every infinite schedule h...

Yu-Tian Ye, Kai-Zhao Liu · 3 citations
#machine learning Preprint Sep 2026

Improved Gradient Descent Lower Bounds Beyond Nesterov

We study how far gradient descent (GD) can be accelerated by predetermined stepsizes in smooth convex optimization. Going beyond the classical $\Omega(n^{-2})$ first-order oracle lower bound of Nemirovsky and Yudin (1983), we prove an $\Omega(n^{-1.6342})$ non-anytime lower bound and an $\Omega(n^{-1.2408})$ anytime lo...

Yu-Tian Ye, Kai-Zhao Liu · 6 citations

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