{
  "abstract": "We study stochastic bandits without knowledge of reward scales or tail parameters. Almost-sure regret guarantees describe eventual learning but do not quantify expected performance or the risk of large regret in a finite run. We introduce $\\texttt{EL-F}$, an anytime empirical-likelihood (EL) extension of the $g$-Forcing policy of Cowan and Katehakis (2020), and characterize its performance at three levels. First, for integrable rewards and non-decreasing, diverging exploration schedules $g$ with vanishing increments, $\\texttt{EL-F}$ preserves the $g$-Forcing asymptotics for pseudo-regret $R(T)$: $R(T)/g(T)\\to\\sum_{i:Δ_i>0}Δ_i$ almost surely as $T\\to\\infty$, where $Δ_i$ is the suboptimality gap of arm $i$. Second, on every sub-exponential instance, for non-decreasing $g(t)=ω(\\log t)$ satisfying a mild feasibility condition, expected pseudo-regret is at most $g(T)\\sum_{i:Δ_i>0}Δ_i+C_{\\underline{P}}$, where $C_{\\underline{P}}$ is an instance-dependent constant independent of $T$. Moreover, we also establish finite-time tail bounds with super-polynomial decay in regret beyond the forced-exploration budget. For slowly varying $g$, we determine the exact exponent of linear regret deviations on two-armed Gaussian instances with common variance and establish a matching lower bound among policies satisfying the same expected-regret budget on every such Gaussian instance. These quantitative guarantees also cover the greedy variant obtained at zero EL radius. A fixed positive radius introduces local optimism while preserving the leading asymptotic regret. We establish coupled pathwise dominance over the greedy variant in two-armed bandits with a deterministic suboptimal arm. Experiments demonstrate reductions in prolonged suboptimal allocation compared with $g$-Forcing on challenging instances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18055",
  "author_total": 3,
  "authors": [
    {
      "name": "Pratham Gupta"
    },
    {
      "name": "Alhad Sethi"
    },
    {
      "name": "Shubhada Agrawal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6fs3r6e6jtk2e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18055",
  "fulltext_url": null,
  "id": "6fs3r6e6jtk2e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18055",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1803|Advanced Bandit Algorithms Research"
    ]
  ],
  "openalex": "W7221768973",
  "pdf_url": "https://arxiv.org/pdf/2610.18055",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6fs3r6e6jtk2e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.18055",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18055"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Reliable Scale-Free Bandits via Empirical Likelihood",
  "title_text": "Reliable Scale-Free Bandits via Empirical Likelihood",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/6fs3r6e6jtk2e",
  "venue": "arXiv",
  "versions": []
}