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We resolve this open question. Leveraging a new Lyapunov function and designing new algorithms, we achieve $O(\sqrt{\ell(0)} R / \sqrt{\varepsilon})$ oracle complexity for small-$\varepsilon$ and virtually any $\ell$. For instance, for $(L_{0},L_{1})$-smoothness, our bound $O(\sqrt{L_0} R / \sqrt{\varepsilon})$ is provably optimal in the small-$\varepsilon$ regime and removes all non-constant multiplicative factors present in prior accelerated algorithms.
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG) |
| Cite as: | arXiv:2508.06884 [math.OC] |
| (or arXiv:2508.06884v2 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2508.06884 arXiv-issued DOI via DataCite |
From: Alexander Tyurin [view email]
[v1]
Sat, 9 Aug 2025 08:28:06 UTC (73 KB)
[v2]
Thu, 21 May 2026 04:59:24 UTC (326 KB)
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