{
  "abstract": "This paper establishes an entropy-regularized reinforcement learning (ERRL) framework for the continuous-time consumption-investment problem under a regime-switching market model with general utility functions. By incorporating randomized exploratory policies and Shannon entropy regularization into the stochastic optimal control formulation, we derive closed-form representations for the optimal exploratory consumption and investment strategies. Specifically, the optimal investment strategy follows a multivariate Gaussian distribution, whereas the optimal consumption strategy takes the form of a Gibbs measure---which specializes to a Gamma distribution under logarithmic utility and a non-standard exponential distribution under power utility. Crucially, our theoretical analysis reveals that the classical deterministic optimal decisions correspond to the mode---rather than the mean---of these exploratory distributions. Furthermore, we establish the convergence of the exploratory value function to its classical unregularized counterpart as the temperature parameter vanishes. For algorithmic design, we develop a continuous-time q-learning framework grounded in a novel continuous-time q-function, prove the policy improvement theorem, and establish martingale characterizations for both on-policy and off-policy learning. We find that parameterizing the actor network based on theoretical distribution families can help accelerate convergence and enhance numerical stability. Furthermore, numerical experiments across regime-switching environments provide empirical support for our theoretical findings, demonstrating stable loss convergence as well as the monotonicity and concavity of the learned value functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01046",
  "author_total": 4,
  "authors": [
    {
      "name": "Congde Hu"
    },
    {
      "name": "Danping Li"
    },
    {
      "name": "Xun Li"
    },
    {
      "name": "Yijie Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9dhk7tsxhha0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01046",
  "fulltext_url": null,
  "id": "e9dhk7tsxhha0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01046",
  "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",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01046",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9dhk7tsxhha0.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01046",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01046"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Entropy-Regularized Reinforcement Learning for the Regime-Switching Consumption-Investment Problem",
  "title_text": "Entropy-Regularized Reinforcement Learning for the Regime-Switching Consumption-Investment Problem",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/e9dhk7tsxhha0",
  "venue": "arXiv",
  "versions": []
}