{
  "abstract": "We develop a derivative-free temporal-difference (TD) framework for calibrating black-box simulators using one-step transitions from a target system and noisy simulator-generated continuation values. The calibration parameter is defined through Bellman orthogonality, recovering the physical parameter under correct simulator specification and yielding a near-optimal $L_2$ approximation of the policy value under misspecification. We propose three TD algorithms based on random-direction finite differences, distinguished by their query costs and reuse of noisy simulator evaluations. We establish almost-sure convergence, last-iterate mean-square error bounds, and central limit theorems for Polyak-Ruppert averages across four query-noise regimes. Our analysis reveals a specification-dependent bias phenomenon: for two algorithms, the finite-difference bias of the TD estimating equation vanishes at the calibration target under correct specification, even when the gradient surrogate remains biased. This permits a fixed perturbation radius and rate exponents approaching $1/2$ in the simulator rollout budget, whereas misspecification generally recovers the classical Kiefer-Wolfowitz rates. We also develop a few-replicate online bootstrap that yields Student-$t$ calibrated confidence intervals under negligible query noise, and identify a covariance mismatch that can invalidate conventional multiplier inference along Markov trajectories. Finally, a second-stage TD recursion corrects the remaining value discrepancy without additional simulator queries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35311",
  "author_total": 5,
  "authors": [
    {
      "name": "Min Zeng"
    },
    {
      "name": "Xin Wen"
    },
    {
      "name": "Xi Chen"
    },
    {
      "name": "Yichen Zhang"
    },
    {
      "name": "Wen-Xin Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cmjpxm4kjh7w9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35311",
  "fulltext_url": null,
  "id": "cmjpxm4kjh7w9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35311",
  "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",
      "1803|Simulation Techniques and Applications"
    ]
  ],
  "openalex": "W7223805866",
  "pdf_url": "https://arxiv.org/pdf/2610.35311",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cmjpxm4kjh7w9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:49Z",
      "native_id": "2610.35311",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35311"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Temporal-Difference Calibration of Black-Box Simulators",
  "title_text": "Temporal-Difference Calibration of Black-Box Simulators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/cmjpxm4kjh7w9",
  "venue": "arXiv",
  "versions": []
}