{
  "abstract": "Policy mirror descent (PMD) has a mature finite-time theory in discounted Markov decision processes (MDPs), but less is known in the average-reward setting, a more natural objective for many control applications. We give a finite-time, finite-sample analysis of PMD in ergodic average-reward MDPs built around a single master recursion that governs convergence for any critic, without external regularization. Its specializations yield linear rates for exact, inexact-tabular, and linear function approximation (LFA) updates, with a superlinear regime for exact PMD. We complement these convergence results with end-to-end sample complexities of order $t_{\\mathrm{mix}}^3/\\varepsilon^2$ in both tabular ($|S||A|$-dependent) and LFA ($d$-dependent) settings. Our LFA sample complexity sharpens the prior best $t_{\\mathrm{mix}}^5$ mixing dependence to $t_{\\mathrm{mix}}^3$, and matching information-theoretic lower bounds establish that the critic's $t_{\\mathrm{mix}}^3/\\varepsilon^2$ sample complexity is unimprovable in both settings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04117",
  "author_total": 2,
  "authors": [
    {
      "name": "Enes Arda"
    },
    {
      "name": "Atilla Eryilmaz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4x5gbn4gqman.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04117",
  "fulltext_url": null,
  "id": "d4x5gbn4gqman",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04117",
  "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": "W7220678134",
  "pdf_url": "https://arxiv.org/pdf/2610.04117",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4x5gbn4gqman.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04117",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04117"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Sharp Convergence and Sample Complexity of Policy Mirror Descent for Average-Reward MDPs",
  "title_text": "Sharp Convergence and Sample Complexity of Policy Mirror Descent for Average-Reward MDPs",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d4x5gbn4gqman",
  "venue": "arXiv",
  "versions": []
}