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We study how far gradient descent (GD) can be accelerated by predetermined nonnegative stepsizes in smooth convex optimization.
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We study how far gradient descent (GD) can be accelerated by predetermined nonnegative stepsizes in smooth convex optimization. Writing $p_{\mathrm{sil}}=\log_2(1+\sqrt{2})$, we prove an $Ω\left(n^{-p_{\mathrm{sil}}-O(\sqrt{\log\log n/\log n})}\right)$ non-anytime lower bound. In the anytime setting, every infinite nonnegative schedule has infinitely many horizons with error $Ω\left(n^{-\frac{2p_{\mathrm{sil}}}{1+p_{\mathrm{sil}}}-O(\sqrt{\log\log n/\log n})}\right)$. Together with the silver-schedule upper bound [Altschuler and Parrilo, 2025] and the anytime upper bound [Zhang et al., 2025],...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.09152v1 · Indexed about 2 hours ago