Conformal-Style Quantile Analyses for Stochastic Bandits
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913101501169664 |
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| author | Du, Chengyu Xu, Mengfan |
| author_facet | Du, Chengyu Xu, Mengfan |
| contents | Stochastic bandit algorithms are usually analyzed under a mean-reward criterion, yet many problems favor arms with strong upper-tail performance, which we study herein. For a fixed miscoverage level \(α\), the natural upper-tail target of arm \(j\) is the upper endpoint \(F_j^{-1}(1-α/2)\) of a central prediction interval. This target can rank arms differently from their means, creating a central mismatch with the classical bandit objective. To this end, we propose ACP-UCB1, a conformal-style policy that combines an adaptive conformal estimate of the upper endpoint with a UCB-type optimism bonus. The technical challenge is that the conformity scores used by ACP-UCB1 are recomputed from evolving empirical quantile estimates and evaluated at an adaptive level. We control this endpoint through reward-quantile concentration, a perturbation argument for recomputed score quantiles, and deterministic localization of the adaptive level. ACP-UCB1 achieves logarithmic upper-quantile regret with per-arm contribution \(O(\nicefrac{\log n}{Δ_j^{\mathrm{ACP}}})\). We also provide metric-specific regret decompositions comparing ACP-UCB1 with UCB1 and use numerical experiments to validate performance and improvement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07115 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conformal-Style Quantile Analyses for Stochastic Bandits Du, Chengyu Xu, Mengfan Machine Learning Stochastic bandit algorithms are usually analyzed under a mean-reward criterion, yet many problems favor arms with strong upper-tail performance, which we study herein. For a fixed miscoverage level \(α\), the natural upper-tail target of arm \(j\) is the upper endpoint \(F_j^{-1}(1-α/2)\) of a central prediction interval. This target can rank arms differently from their means, creating a central mismatch with the classical bandit objective. To this end, we propose ACP-UCB1, a conformal-style policy that combines an adaptive conformal estimate of the upper endpoint with a UCB-type optimism bonus. The technical challenge is that the conformity scores used by ACP-UCB1 are recomputed from evolving empirical quantile estimates and evaluated at an adaptive level. We control this endpoint through reward-quantile concentration, a perturbation argument for recomputed score quantiles, and deterministic localization of the adaptive level. ACP-UCB1 achieves logarithmic upper-quantile regret with per-arm contribution \(O(\nicefrac{\log n}{Δ_j^{\mathrm{ACP}}})\). We also provide metric-specific regret decompositions comparing ACP-UCB1 with UCB1 and use numerical experiments to validate performance and improvement. |
| title | Conformal-Style Quantile Analyses for Stochastic Bandits |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.07115 |