{
  "abstract": "Many modern learning systems are used not to select a single best action, but to sample diverse high-quality outputs. Examples include entropy-regularized reinforcement learning, RLHF, and reward-guided generative modeling. Motivated by these settings, we study tilted sampling: an online learning problem in which the goal is to sample from the Gibbs distribution induced by an unknown reward function. We define sampling regret as the temperature-normalized cumulative KL divergence between the learner's distribution and the Gibbs target, corresponding to the suboptimality gap in entropy-regularized reward maximization. Our framework generalizes recent sampling-based and KL-regularized formulations in bandits and reinforcement learning. Our main contribution is a general regret framework that captures the different uncertainty structure of tilted sampling and classical regret minimization. While standard regret scales as $\\widetilde{O}(\\sqrt{T})$ due to first-order uncertainty, sampling regret is governed by squared confidence widths, yielding logarithmic-in-$T$ regret in standard settings at fixed temperature. We develop sampling analogues of UCB and Thompson sampling (UCS and TS$^2$) and provide unified regret decompositions that explain and extend recent logarithmic guarantees, including the first Bayesian sampling-regret decomposition based on new bounds for posterior-random Gibbs distributions. Our results show that learning to sample from a soft-optimal distribution is statistically distinct from learning to identify a hard optimum.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21908",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohammad Pedramfar"
    },
    {
      "name": "Siamak Ravanbakhsh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/872d5zd49g5th.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21908",
  "fulltext_url": null,
  "id": "872d5zd49g5th",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21908",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7222618300",
  "pdf_url": "https://arxiv.org/pdf/2610.21908",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/872d5zd49g5th.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21908",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21908"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "The Tilted Sampling Problem: Optimism, Posterior Sampling, and Logarithmic Regret",
  "title_text": "The Tilted Sampling Problem: Optimism, Posterior Sampling, and Logarithmic Regret",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/872d5zd49g5th",
  "venue": "arXiv",
  "versions": []
}