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arXiv 2512.04697math.OCcs.LGq-fin.CP
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连续时间强化学习用于多 regime 最优化切换

Continuous-time reinforcement learning for optimal switching over multiple regimes

Department of Applied Mathematics, The Hong Kong Polytechnic University(应用数学系,香港理工大学);School of Mathematics and Statistics, University of Sydney(数学与统计学学院,悉尼大学)

Yijie Huang, Mengge Li, Xiang Yu, Zhou Zhou

AI总结:

本文提出了一种基于连续时间强化学习的多 regime 最优化切换方法,通过熵正则化和马尔可夫链生成矩阵实现策略优化,并利用神经网络验证了算法有效性。

摘要:

本文研究了连续时间强化学习(RL)在多个 regime 中的最优切换问题。我们考虑了一种在熵正则化下的探索性公式,其中智能体通过关联的连续时间有限状态马尔可夫链的生成矩阵,随机化切换的时间和 regime 的选择。我们建立了所关联的汉密尔顿-雅可比-贝尔曼(HJB)方程组的合理性,并提供了最优策略的特征化。通过分析方程组,我们严格建立了策略改进和策略迭代的收敛性。我们还展示了在探索性公式中,当温度参数消失时,价值函数向经典公式中的价值函数收敛。最后,通过调用基于鞅特征化的策略评估,设计并实现了强化学习算法。我们的数值例子借助神经网络展示了所提出 RL 算法的有效性。

英文摘要:

This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes. We consider a type of exploratory formulation under entropy regularization where the agent randomizes both the timing of switches and the selection of regimes through the generator matrix of an associated continuous-time finite-state Markov chain. We establish the well-posedness of the associated system of Hamilton-Jacobi-Bellman (HJB) equations and provide a characterization of the optimal policy. The policy improvement and the convergence of the policy iterations are rigorously established by analyzing the system of equations. We also show that the value function in the exploratory formulation converges to the one in the classical formulation as the temperature parameter vanishes. Finally, a model-free reinforcement learning algorithm is devised and implemented by invoking the policy evaluation based on the martingale characterization. Our numerical examples with financial applications illustrate the effectiveness and efficiency of the proposed RL algorithm.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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