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Multi-Armed Bernoulli Bandits via Minimax Single-Arm Stopping — arXiv:2609.22690

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.22690
License (as archived): CC0-1.0
Archived: 2026-10-09T07:06:46.809Z
SHA-256 of the archived text: 610ac8dc9dfac97335960cec61454314c1af6c20692adca6767837a534a52a38
Stable URL of this page: https://metraipolis.com/documento/dc_bfc0bda97ccd

How to cite

Multi-Armed Bernoulli Bandits via Minimax Single-Arm Stopping — arXiv:2609.22690 — arXiv (en), https://arxiv.org/abs/2609.22690 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bfc0bda97ccd (Metraipolis archive dc_bfc0bda97ccd, sha256 610ac8dc9dfac97335960cec61454314c1af6c20692adca6767837a534a52a38)

BibTeX

@misc{dcbfc0bda97ccd,
  title = {Multi-Armed Bernoulli Bandits via Minimax Single-Arm Stopping — arXiv:2609.22690},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.22690},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bfc0bda97ccd; sha256 610ac8dc9dfac97335960cec61454314c1af6c20692adca6767837a534a52a38},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.22690. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We develop an index policy for finite-horizon Bernoulli multi-armed bandits from minimax solutions to single-arm bandit (SAB) problems. Each SAB problem involves choosing between an unknown Bernoulli arm and a known reward. We show that minimizing worst-case regret of SAB problems over all non-anticipative policies admits an exact semi-infinite linear programming formulation. The resulting stopping policies offer a natural way to compare arms: the higher the known reward against which a policy continues sampling, the more promising the unknown arm. We turn this intuition into indices based on cumulative continuation probabilities, with a monotone adjustment and a reward-shortfall cap. By relating index errors to the regret of single-arm stopping policies, we establish a distribution-free regret bound of $4.45\sqrt{KT}+10.75K$ for $K$ arms and horizon $T$. This bound matches the minimax-optimal regret order established in the literature. The guarantee extends to rewards supported on $[0,1]$ through Bernoulli randomization. We also provide a finite-grid implementation with quantified approximation loss. In numerical experiments, the SAB-based index policy achieves lower worst-case regret than every tested benchmark policy across all evaluated numbers of arms and horizons, while closely matching the grid-based MAB minimax policy in the two-arm setting.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-22 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG) ; Optimization and Control (math.OC); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2609.22690 — 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 2026-10-09T06:58:09.212Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-22?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).