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Instance-dependent sequential limits as an exact information ledger — arXiv:2610.42133

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.42133
License (as archived): CC0-1.0
Archived: 2026-11-02T07:51:06.453Z
SHA-256 of the archived text: 79db851ce97686e97ef15a01da9d030989445d144836e1dcdb3b8f46c01f7f67
Stable URL of this page: https://metraipolis.com/documento/dc_d89bc41adafa

How to cite

Instance-dependent sequential limits as an exact information ledger — arXiv:2610.42133 — arXiv (en), https://arxiv.org/abs/2610.42133 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d89bc41adafa (Metraipolis archive dc_d89bc41adafa, sha256 79db851ce97686e97ef15a01da9d030989445d144836e1dcdb3b8f46c01f7f67)

BibTeX

@misc{dcd89bc41adafa,
  title = {Instance-dependent sequential limits as an exact information ledger — arXiv:2610.42133},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.42133},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d89bc41adafa; sha256 79db851ce97686e97ef15a01da9d030989445d144836e1dcdb3b8f46c01f7f67},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.42133. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Instance-dependent limits for bandit regret, sequential tests, best-arm identification and Markov decision processes are proved by one chain. It runs from a divergence decomposition through data processing to a statistic, a testing step that turns a class guarantee into a requirement on the history, and optimization over alternatives and allocations. Only the first step is an identity. This work writes the chain as an exact ledger. By the chain rule, data processing loses exactly a conditional divergence, which vanishes for arms in natural exponential families at the per-arm counts and reward sums. A one-parameter family of martingale identities extends the decomposition to every tilt between two instances. The classical limits follow by relaxations with named defects. All defects but the asymptotic step's can be computed from an algorithm's own runs, the uniform quantification's only when the class guarantee is a number. On seven published sources, from movie ratings to engine replacement, the ledger locates the difference between standard algorithms and the classical limits. For identification among trained models and for Wald's test the largest term is usually the uniform quantification's.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Information Theory (cs.IT); Statistics Theory (math.ST); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2610.42133 — 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 2026-11-02T07:40:00.226Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).