Entropy-Regularized Reinforcement Learning for the Regime-Switching Consumption-Investment Problem
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.
Related
- Consumption and Investment with Multiple Job-Switching Opportunities
- Continuous-Time Mean-Variance Portfolio Selection Reinforcement Learning Problems for a Markov Regime-Switching System with No-Shorting Constraints
- Optimal investment and consumption for financial markets with jumps under transaction costs
- Optimal Annuitization, Consumption, and Investment with Costly Capital Injections
- Consumption and Investment When Welfare Floors Change over Time
BibTeX
@misc{hu2026entropyregularized,
title = {{Entropy-Regularized Reinforcement Learning for the Regime-Switching Consumption-Investment Problem}},
author = {Congde Hu and Danping Li and Xun Li and Yijie Zeng},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01046},
eprint = {2611.01046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01046},
}
RIS
TY - UNPB
TI - Entropy-Regularized Reinforcement Learning for the Regime-Switching Consumption-Investment Problem
AU - Congde Hu
AU - Danping Li
AU - Xun Li
AU - Yijie Zeng
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01046
UR - https://arxiv.org/abs/2611.01046
AB - 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.
ER -