{
  "abstract": "This work studies an entropy-based estimator of Kullback-Leibler (KL) divergence constructed from normalized importance weights. We prove a universal finite-sample bound showing that its expectation can exceed the target-proposal KL divergence by at most $\\log 2$ for any sample size. We then characterize the KL divergence between the distribution induced by importance-weighted resampling and the proposal, showing that it is upper bounded by both the expectation of the entropy-based estimator and the target-proposal KL divergence. Importantly, these bounds require neither bounded importance weights nor finite higher moments. We apply these results to test-time alignment of generative models via Soft Best-of-$N$ sampling, an importance-sampling-based scaling technique proposed by Verdun et al. (2025), and to relative entropy coding, obtaining finite-sample policy-divergence certificates and moment-free bounds on coding cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12851",
  "author_total": 3,
  "authors": [
    {
      "name": "Buu Phan"
    },
    {
      "name": "Lester Mackey"
    },
    {
      "name": "David Alvarez-Melis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aa0q74vywwe7e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12851",
  "fulltext_url": null,
  "id": "aa0q74vywwe7e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12851",
  "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",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7221539199",
  "pdf_url": "https://arxiv.org/pdf/2610.12851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aa0q74vywwe7e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:46Z",
      "native_id": "2610.12851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Universal Bounds for Self-Normalized Kullback-Leibler Estimation",
  "title_text": "Universal Bounds for Self-Normalized Kullback-Leibler Estimation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:46Z",
  "url": "https://research.draconitic.com/paper/aa0q74vywwe7e",
  "venue": "arXiv",
  "versions": []
}