# Entropy Regularized Reinforcement Learning for Zero-Sum Stochastic Differential Games in a Regime-Switching Jump-Diffusion Process

arXiv: https://arxiv.org/abs/2606.28669 · HTML: https://mlsanity.com/paper/2606.28669/

## Key facts

- Cited by 1 papers in the map (data through 14 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.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 9 of 9)

- [Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approach](https://mlsanity.com/paper/2108.06655/) (2021)
- [Entropy Regularization for Mean Field Games with Learning](https://mlsanity.com/paper/2010.00145/) (2020)
- [Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks](https://mlsanity.com/paper/2102.11379/) (2021)
- [Exploratory LQG Mean Field Games with Entropy Regularization](https://mlsanity.com/paper/2011.12946/) (2020)
- [Convergence of Policy Iteration for Entropy-Regularized Stochastic Control Problems](https://mlsanity.com/paper/2209.07059/) (2022)
- [Linear-Quadratic Stochastic Stackelberg Differential Games for Jump-Diffusion Systems](https://mlsanity.com/paper/2007.05895/) (2020)
- [Linear quadratic leader-follower stochastic differential games for mean-field switching diffusions](https://mlsanity.com/paper/2208.00347/) (2022)
- [Solving a class of zero-sum stopping game with regime switching](https://mlsanity.com/paper/2303.15730/) (2023)
- [Risk-Minimizing Two-Player Zero-Sum Stochastic Differential Game via Path Integral Control](https://mlsanity.com/paper/2308.11546/) (2023)

## Built on by (most cited first, 1 of 1)

- [Continuous-Time Reinforcement Learning for N-Player Stochastic Differential Games with Exploratory Policies](https://mlsanity.com/paper/2607.19928/) (2026)

## 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.