{
  "abstract": "We propose an algorithm to sample from composite log-concave distributions over $\\mathbb{R}^d$, i.e., densities of the form $π\\propto e^{-f-g}$, assuming access to gradient evaluations of $α_f$-convex $f$ and a restricted Gaussian oracle (RGO) for $α_g$-convex $g$, where $α_g \\ge 0$. The latter requirement means that we can easily sample from the density $\\text{RGO}_{g,h,y}(x) \\propto \\exp(-g(x) -\\frac{1}{2h}||y-x||^2)$, which is the sampling analogue of the proximal operator for $g$. If $f + g$ is $α$-convex and $f$ is $β$-smooth, our sampler achieves $\\varepsilon$ error in total variation distance using $\\widetilde{\\mathcal O}(κ\\sqrt d \\log^4(1/\\varepsilon))$ oracle calls where $κ:= 1 \\vee β/α$, with $0\\le α_g \\le β$ and $α:= α_f + α_g > 0$, which matches prior state-of-the-art results for the case $g=0$. We further extend our results to cases where (1) $π$ is non-log-concave but satisfies a Poincaré or log-Sobolev inequality, and (2) $f$ is non-smooth but Lipschitz.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.12461",
  "author_total": 2,
  "authors": [
    {
      "name": "Linghai Liu"
    },
    {
      "name": "Sinho Chewi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/770x0249yvagj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.12461",
  "fulltext_url": null,
  "id": "770x0249yvagj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.12461",
  "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.DS"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
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      "arxiv",
      "stat.TH"
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    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
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  "openalex": "W7160984462",
  "pdf_url": "https://arxiv.org/pdf/2605.12461",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/770x0249yvagj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2605.12461",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.12461"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A proximal gradient algorithm for composite log-concave sampling",
  "title_text": "A proximal gradient algorithm for composite log-concave sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/770x0249yvagj",
  "venue": "arXiv",
  "versions": []
}