Silver Rate Is (Almost) Optimal for Gradient Descent — Paper

Abstract

-cross Abstract: 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 has infinitely many horizons with error $\Omega\left(n^{-\frac{2p_{\mathrm{sil}}}{1+p_{\mathrm{sil}}}-O(\sqrt{\log\log n/\log n})}\right)$. Together with the silver-schedule upper bound [Altschuler and Parrilo, 2025] and the anytime upper bound [Zhang et al., 2025], our results determine the optimal polynomial convergence exponents in both settings.

Authors 2

Yuhan Ye, Kaizhao Liu

Specification

Official page: arxiv.org/abs/2609.09152
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Arxiv announce type: replace
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
arXiv id: 2609.09152
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Categories: math.OC, cs.LG
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
PDF: arxiv.org/pdf/2609.09152
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Primary category: math.OC
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 2 h agohigh

Each value shows its source, tier and observation time. Conflicting claims are kept side by side and flagged — never averaged. How AI Atlas records facts →

Provenance

Attributed facts

9

Source tiers

T19

Freshest observation

2 h ago

Conflicts

None

No models linked to this paper yet.

Authors: Yuhan Ye, Kaizhao Liu

As of

Rewind the record: see this entity's attributes exactly as AI Atlas knew them on a given day.

Claim history · arXiv id

1 claims · 1 propertiesShow all properties

arXiv idarxiv_id1

Claim history for arXiv id
Value	Valid from → to	Status	Source	Confidence	Extractor
2609.09152	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperSilver Rate Is (Almost) Optimal for Gradient Descent
New paper: Silver Rate Is (Almost) Optimal for Gradient Descent
arxiv
rss.arxiv.org

Full timeline →

Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	6 min ago	1

Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.