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Near-Optimal List Replicability from Littlestone Dimension — arXiv:2610.32853

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.32853
License (as archived): CC0-1.0
Archived: 2026-10-26T20:13:49.297Z
SHA-256 of the archived text: fecf20660b8743258209e69a8f2bbb36716da4ba805c6854fff9106e9eb02436
Stable URL of this page: https://metraipolis.com/documento/dc_5239b3d6dfd8

How to cite

Near-Optimal List Replicability from Littlestone Dimension — arXiv:2610.32853 — arXiv (en), https://arxiv.org/abs/2610.32853 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_5239b3d6dfd8 (Metraipolis archive dc_5239b3d6dfd8, sha256 fecf20660b8743258209e69a8f2bbb36716da4ba805c6854fff9106e9eb02436)

BibTeX

@misc{dc5239b3d6dfd8,
  title = {Near-Optimal List Replicability from Littlestone Dimension — arXiv:2610.32853},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.32853},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_5239b3d6dfd8; sha256 fecf20660b8743258209e69a8f2bbb36716da4ba805c6854fff9106e9eb02436},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.32853. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the list replicability number in the realizable PAC learning framework and prove that every concept class $H$ over a countable domain with Littlestone dimension $d$ and dual VC dimension $v^*$ satisfies \[ \mathrm{LR}(H)\leq 2^{O(d\min\{\log d,v^*\})}. \] This matches the worst-case lower bound of $2^{\Omega(d)}$ up to a logarithmic factor in the exponent and exponentially improves the previous best upper bound $\mathrm{LR}(H)\le 2^{2^{O(d)}}$ of Bun, Livni, and Moran [FOCS 2020]. Unlike earlier bounds of $2^{O_\epsilon(d^2)}$ for fixed accuracy $\epsilon>0$ implied by the work of Ghazi, Golowich, Kumar, and Manurangsi [STOC 2021] and Lyu [STOC 2026], our bound is independent of $\epsilon$. The $2^{O(d\log d)}$ bound follows from a new inductive framework for bounding list replicability that builds on the recent notion of irreducibility from differentially private learning. The $2^{O(dv^*)}$ bound follows from a simple globally stable learner that takes the majority vote of multiple empirical risk minimizers, with stability established using tools from stable regularity.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2610.32853 — 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 2026-10-26T19:49:03.434Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).