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Entropy-Regularized Reinforcement Learning for the Regime-Switching Consumption-Investment Problem — arXiv:2611.01046

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01046
License (as archived): CC0-1.0
Archived: 2026-11-03T18:36:39.442Z
SHA-256 of the archived text: 51a50720bbcec77b6848ea099e7e505ef0ea6fb8c4b9417b9ccceb27f1044157
Stable URL of this page: https://metraipolis.com/documento/dc_00df755fbf58

How to cite

Entropy-Regularized Reinforcement Learning for the Regime-Switching Consumption-Investment Problem — arXiv:2611.01046 — arXiv (en), https://arxiv.org/abs/2611.01046 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_00df755fbf58 (Metraipolis archive dc_00df755fbf58, sha256 51a50720bbcec77b6848ea099e7e505ef0ea6fb8c4b9417b9ccceb27f1044157)

BibTeX

@misc{dc00df755fbf58,
  title = {Entropy-Regularized Reinforcement Learning for the Regime-Switching Consumption-Investment Problem — arXiv:2611.01046},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01046},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_00df755fbf58; sha256 51a50720bbcec77b6848ea099e7e505ef0ea6fb8c4b9417b9ccceb27f1044157},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01046. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Optimization and Control (math.OC).
Pagina del lavoro: https://arxiv.org/abs/2611.01046 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:12:54.470Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).