{
  "abstract": "We develop a new low-accuracy sampler, called smoothed Picard Hamiltonian Monte Carlo, which combines Gaussian smoothing, Picard iteration, and higher-order discretization. For a log-concave target $π\\propto \\exp(-V)$ in dimension $d$ satisfying $0 \\prec αI \\preceq \\nabla^2 V \\preceq βI$, with condition number $κ:= β/α$, smoothed Picard HMC returns a sample with $\\sqrt α\\,W_2(\\cdot,π) \\le \\varepsilon$ using $\\widetilde O(κ^2 + κ^{7/6} d^{1/6}/\\varepsilon^{1/3})$ gradient queries. We also prove stronger $W_q$ bounds, and then develop an algorithmic framework, the recursive warm start generator, to upgrade these $W_q$ bounds to stronger divergence guarantees. This produces a warm start for the proximal bouncy particle sampler, introduced in a companion work, leading to a high-accuracy log-concave sampler with complexity $\\widetilde O((κ^{7/6} d^{1/6} + κ^{1/2} d^{1/4})\\mathrm{polylog}(1/\\varepsilon))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06906",
  "author_total": 4,
  "authors": [
    {
      "name": "Fan Chen"
    },
    {
      "name": "Sinho Chewi"
    },
    {
      "name": "Jianfeng Lu"
    },
    {
      "name": "Matthew S Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/apw3d3gr84wxy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06906",
  "fulltext_url": null,
  "id": "apw3d3gr84wxy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06906",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "2613|Markov Chains and Monte Carlo Methods"
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  "pdf_url": "https://arxiv.org/pdf/2609.06906",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/apw3d3gr84wxy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.06906",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06906"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Smoothed Picard Hamiltonian Monte Carlo",
  "title_text": "Smoothed Picard Hamiltonian Monte Carlo",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/apw3d3gr84wxy",
  "venue": "arXiv",
  "versions": []
}