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On the Last-Iterate Convergence of Clipped Gradient Methods — arXiv:2610.21026

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.21026
License (as archived): CC0-1.0
Archived: 2026-10-16T10:25:08.291Z
SHA-256 of the archived text: d429f61fac69a72d6bf4d35c6252bf437f471c86549612be46ebc00c1aff3888
Stable URL of this page: https://metraipolis.com/documento/dc_68e72fff4e5f

How to cite

On the Last-Iterate Convergence of Clipped Gradient Methods — arXiv:2610.21026 — arXiv (en), https://arxiv.org/abs/2610.21026 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_68e72fff4e5f (Metraipolis archive dc_68e72fff4e5f, sha256 d429f61fac69a72d6bf4d35c6252bf437f471c86549612be46ebc00c1aff3888)

BibTeX

@misc{dc68e72fff4e5f,
  title = {On the Last-Iterate Convergence of Clipped Gradient Methods — arXiv:2610.21026},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.21026},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_68e72fff4e5f; sha256 d429f61fac69a72d6bf4d35c6252bf437f471c86549612be46ebc00c1aff3888},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.21026. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In stochastic (strongly) convex optimization, establishing last-iterate convergence guarantees for first-order methods has recently garnered increasing attention, as this not only deepens the theoretical understanding of these algorithms but also aligns more closely with practice. Notably, people have demonstrated that one of the most famous, simple, and popular methods, Stochastic Gradient Descent ($\mathtt{SGD}$), provably achieves last-iterate convergence. However, the existing results may have limited applicability, since they typically rely on strong conditions on the gradient noise (e.g., an exponentially decaying tail) rather than the more realistic heavy-tailed noise. Unfortunately, when faced with heavy-tailed noise, $\mathtt{SGD}$ is known to exhibit undesirable behavior or even fail to converge. To address the challenge of heavy-tailed noise, people have proposed $\mathtt{Clipped}\text{-}\mathtt{SGD}$, an algorithm that combines $\mathtt{SGD}$ with a simple mechanism, gradient clipping. Although $\mathtt{Clipped}\text{-}\mathtt{SGD}$ performs well in practice, its last-iterate convergence property remains highly underexplored. In this work, we prove the first optimal last-iterate rates in high probability for $\mathtt{Clipped}\text{-}\mathtt{SGD}$ under heavy-tailed noise, thereby closing a gap in the literature.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Optimization and Control (math.OC) ; Machine Learning (cs.LG); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2610.21026 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T08:48:02.880Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).