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Reconciling Universal and Uniform Learning with $Q$-Aggregation — arXiv:2609.05041

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.05041
License (as archived): CC0-1.0
Archived: 2026-10-16T23:02:55.422Z
SHA-256 of the archived text: 85d2272ec425a6a03fe9ea70b7389339828cb58fced7a6f18203608ed9141f2e
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How to cite

Reconciling Universal and Uniform Learning with $Q$-Aggregation — arXiv:2609.05041 — arXiv (en), https://arxiv.org/abs/2609.05041 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_73d8cbca16dd (Metraipolis archive dc_73d8cbca16dd, sha256 85d2272ec425a6a03fe9ea70b7389339828cb58fced7a6f18203608ed9141f2e)

BibTeX

@misc{dc73d8cbca16dd,
  title = {Reconciling Universal and Uniform Learning with $Q$-Aggregation — arXiv:2609.05041},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.05041},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_73d8cbca16dd; sha256 85d2272ec425a6a03fe9ea70b7389339828cb58fced7a6f18203608ed9141f2e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.05041. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study regression under bounded responses in terms of excess mean squared error. When the comparator class is finite, this setting is known as model selection aggregation, and achieving minimax excess risk requires improper learning algorithms. Contrary to this, in the universal learning framework no improperness is needed, as simple empirical risk minimization achieves the best-possible exponential learning rate. Hence, the two frameworks suggest different optimal algorithmic principles. This poses the question of best-of-both-worlds guarantees: Are minimax and universal exponential rates achievable by the same algorithm? For finite hypothesis classes, we answer this question in the affirmative by showing that the $Q$-aggregation estimator - which is known to achieve minimax optimal tails - achieves exponential universal rates. A wide range of other estimators and algorithmic principles (ERM, sequential averaging, pruning, and star estimation) do not achieve both. For countably infinite hypothesis classes, we answer the question in the negative by showing that there is an inherent trade-off between achieving exponential universal and minimax uniform rates. This trade-off is exactly traced by combining optimal algorithms from each world using $Q$-aggregation. Besides these results, we prove several additional structural results about universal rates in learning with squared loss.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-07 in stat.ML).
Categorie arXiv: Statistics Theory (math.ST) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2609.05041 — 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 2026-10-16T22:46:53.234Z dalla pagina https://arxiv.org/catchup/stat.ML/2026-09-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).