{
  "abstract": "Temporal-difference (TD) learning underlies many prediction and control algorithms, but can diverge when combined with off-policy learning, bootstrapping, and function approximation. TD with Regularized Corrections (TDRC) is theoretically sound and practically simple, but existing convergence theory covers only the one-step case under i.i.d. sampling, while the Huber Bellman-error formulation has not been extended to TDRC or eligibility traces. In this work, we establish convergence of constrained TDRC($λ$) with diminishing stepsizes and non-i.i.d. off-policy data, for state-dependent and history-dependent $λ$-parameters. We also propose TDRC($λ$)-Huber, which preserves the TDRC($λ$) fixed point while reducing sensitivity to large Bellman errors. For both algorithms, we apply an ODE-based weak-convergence method from stochastic approximation theory. For the nonlinear mean dynamics of TDRC($λ$)-Huber, we give an integral small-gain condition that guarantees uniqueness and global asymptotic stability of the target equilibrium. We then establish convergence of the constrained algorithm, derive computable sufficient conditions for convergence, and identify a regularization-based convergence mechanism shared by linear TDRC($λ$) and TDRC($λ$)-Huber. When the mean TD matrix is positive stable, both constrained algorithms converge under sufficiently strong regularization without requiring positive definiteness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05869",
  "author_total": 3,
  "authors": [
    {
      "name": "Jingyi Jin"
    },
    {
      "name": "Martha White"
    },
    {
      "name": "Hao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/basrvfnzqsjjs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05869",
  "fulltext_url": null,
  "id": "basrvfnzqsjjs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05869",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05869",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/basrvfnzqsjjs.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05869",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05869"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "On Convergence of Gradient Temporal-Difference Learning with Regularized Corrections and Eligibility Traces",
  "title_text": "On Convergence of Gradient Temporal-Difference Learning with Regularized Corrections and Eligibility Traces",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/basrvfnzqsjjs",
  "venue": "arXiv",
  "versions": []
}