Entropy Regularized Reinforcement Learning for Zero-Sum Stochastic Differential Games in a Regime-Switching Jump-Diffusion Process
On the map: Deep reinforcement learning methods → RL theory and sample complexity
Abstract (arXiv)
To address parameter misspecification and sudden structural environmental changes in conventional stochastic differential game (SDG) frameworks, this paper introduces a distributional control approach that characterizes optimal strategies as probability distributions over actions, conditioned on the continuous state, the discrete regime state, and parameters. This forms a reinforcement learning framework for entropy-regularized zero-sum stochastic differential games (ERRL-ZSSDGs) in a regime-switching jump-diffusion process. Using the dynamic programming principle (DPP), we derive the associated coupled systems of Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations, from which equilibrium strategies are expressed via gradients of the value function. For linear-quadratic problems, semi-analytical solutions for both value function and equilibrium strategies are obtained by solving a system of coupled ordinary differential equations (ODEs). In more general settings, an Actor-Critic policy improvement algorithm is developed to approximate the value functions and equilibrium policies across different regimes. The method is applied to an investment game, and numerical examples illustrate the effect of the temperature parameter and regime transitions on optimal policies and values.
Key facts. No citing papers in the map yet (data through 13 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 9 of its 39 references that are in the map. First posted on arXiv 27 Jun 2026.
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References · 9
- 2021Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approachcited by 63
- 2020Entropy Regularization for Mean Field Games with Learningcited by 50
- 2021Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networkscited by 27
- 2020Exploratory LQG Mean Field Games with Entropy Regularizationcited by 11
- 2022Convergence of Policy Iteration for Entropy-Regularized Stochastic Control Problemscited by 7
- 2020Linear-Quadratic Stochastic Stackelberg Differential Games for Jump-Diffusion Systemscited by 2
- 2022Linear quadratic leader-follower stochastic differential games for mean-field switching diffusionscited by 2
- 2023Solving a class of zero-sum stopping game with regime switchingcited by 1
- 2023Risk-Minimizing Two-Player Zero-Sum Stochastic Differential Game via Path Integral Controlcited by 1
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