Author

Yu-Tian Ye

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Preprint Sep 2026

Silver Rate Is (Almost) Optimal for Gradient Descent: The Strongly Convex Case

We study gradient descent with predetermined nonnegative stepsizes on smooth strongly convex functions. Let $p_{\mathrm{sil}}=\log_2(1+\sqrt2)$ and $\kappa$ be the condition number. We prove the iteration lower bound $\Omega\left(\kappa^{\frac{1}{p_{\mathrm{sil}}}-o(1)}\log\frac1\delta\right)$ for both relative squared...

Kai-Zhao Liu, Yu-Tian Ye · 0 citations

#machine learning Preprint Sep 2026

Silver Rate Is (Almost) Optimal for Gradient Descent

Together with the silver-schedule upper bound and the anytime upper bound, the results determine the optimal polynomial convergence exponents in both settings.

Yu-Tian Ye, Kai-Zhao Liu · 3 citations

#machine learning Preprint Sep 2026

Improved Gradient Descent Lower Bounds Beyond Nesterov

The anytime lower bound shows that the rate of non-anytime silver schedules (Altschuler and Parrilo, 2025; Grimmer et al., 2025) is unattainable in the anytime setting, and establishes a strict separation between the two settings.

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