{
  "abstract": "Policy mirror descent (PMD) enjoys fast convergence in regularized Markov decision processes (MDPs), but existing guarantees often rely on exact or increasingly accurate policy evaluation. We analyze PMD coupled with a persistent critic advanced by one temporal-difference (TD) update. For finite discounted MDPs, we establish global linear convergence in value for exact coordinate-wise Bellman updates, with any positive constant actor stepsize and arbitrary finite critic initialization. The proof combines a resolvent-based auxiliary distribution with a decaying Bellman-violation correction and a potential weighted by inverse coordinate weights. We then study stochastic TD-PMD with general strongly convex mirror maps under a single off-policy Markov trajectory. With suitably chosen constant stepsizes and a finite-batch TD update, the method achieves an expected value gap of $ε$ after $\\widetilde{O}(1/((1-γ)^5 \\widetildeσ_b ε))$ transitions. The stochastic analysis relies on the trajectory-wise Lipschitz continuity of the regularizer, derived from uniform bounds on vertex Bregman divergences, together with a visitation-weighted resolvent estimate for signed critic-error propagation that yields an inverse-linear dependence on behavior coverage $\\widetildeσ_b$. In contrast to many prior guarantees for regularized policy optimization, our sample-complexity guarantee holds without trajectory resets, generative-model access, or nested policy-evaluation loops. Numerical results are consistent with the theoretical convergence analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39837",
  "author_total": 4,
  "authors": [
    {
      "name": "Qipei Chen"
    },
    {
      "name": "Wenye Li"
    },
    {
      "name": "Yule Sun"
    },
    {
      "name": "Ke Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1erd10jtwbrbp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39837",
  "fulltext_url": null,
  "id": "1erd10jtwbrbp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39837",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1702|Reinforcement Learning in Robotics"
    ]
  ],
  "openalex": "W7215101407",
  "pdf_url": "https://arxiv.org/pdf/2609.39837",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1erd10jtwbrbp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39837",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39837"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Fast Regularized Policy Mirror Descent with One-Step TD Updates",
  "title_text": "Fast Regularized Policy Mirror Descent with One-Step TD Updates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/1erd10jtwbrbp",
  "venue": "arXiv",
  "versions": []
}