{
  "abstract": "Diffusion policies represent multimodal action distributions, but an advantage-weighted update does not specify how to sample from the resulting target distribution. We propose Schrödinger--Föllmer Actor--Critic (SFAC), an offline-to-online reinforcement learning (RL) method for Kullback--Leibler (KL)-regularized policy improvement through conditional diffusion. A minimax Bellman critic estimates the advantage function, which defines an exponentially tilted target policy. A Doob $h$-transform expresses this update as a correction to the reference diffusion drift. We derive a posterior-mean representation of the correction and estimate it using paired self-normalized importance sampling (SNIS). Supervised regression on these drift targets updates the neural actor without critic action gradients. In the small-update regime, the KL-regularized update follows the natural policy-gradient direction, and the Doob correction represents the same local change in the space of diffusion drifts. Under suitable conditions, we derive finite-sample bounds that separate the effects of critic estimation, neural drift regression, finite-sample SNIS, diffusion discretization, and inherited actor error on expected average policy suboptimality. Synthetic experiments assess the accuracy of approximation to prescribed advantage-tilted targets and sensitivity to sampling budgets. On six offline-to-online continuous-control tasks, a reference-anchored implementation achieves higher final-window returns than those of its corresponding offline initialization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33239",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuling Jiao"
    },
    {
      "name": "Lican Kang"
    },
    {
      "name": "Jerry Zhijian Yang"
    },
    {
      "name": "Jincheng Ying"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/183ddhcg6fb3a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33239",
  "fulltext_url": null,
  "id": "183ddhcg6fb3a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33239",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7214707085",
  "pdf_url": "https://arxiv.org/pdf/2609.33239",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/183ddhcg6fb3a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.33239",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33239"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Schrödinger--Föllmer Actor--Critic: Diffusion Policy Improvement with Finite-Sample Analysis",
  "title_text": "Schrödinger--Föllmer Actor--Critic: Diffusion Policy Improvement with Finite-Sample Analysis",
  "type": "preprint",
  "updated_at": "2026-11-05T15:21:06Z",
  "url": "https://research.draconitic.com/paper/183ddhcg6fb3a",
  "venue": "arXiv",
  "versions": []
}