RL Framework for Zero-Sum Games in Dynamic Environments

Congde Hu, Zhuo Jin, Danping Li, Lin Xu· June 30, 2026 View original

Summary

This paper introduces an entropy-regularized reinforcement learning framework for zero-sum stochastic differential games (ERRL-ZSSDGs) in regime-switching jump-diffusion processes. It addresses parameter misspecification and sudden environmental changes, deriving optimal strategies as probability distributions.

Traditional stochastic differential game (SDG) frameworks often struggle with real-world complexities like inaccurate parameter assumptions and abrupt environmental shifts. To overcome these limitations, a new approach is proposed that uses distributional control to define optimal strategies as probability distributions, conditioned on various state and parameter factors. This forms an entropy-regularized reinforcement learning framework tailored for zero-sum stochastic differential games (ERRL-ZSSDGs) operating within a regime-switching jump-diffusion process. The framework leverages the dynamic programming principle to derive Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations, from which equilibrium strategies can be determined. For simpler linear-quadratic problems, semi-analytical solutions are achievable. For more general scenarios, an Actor-Critic policy improvement algorithm is developed to approximate value functions and policies across different regimes. The method's practical application is demonstrated through an investment game, illustrating how temperature parameters and regime transitions influence optimal strategies.

Why it matters

This research provides a robust framework for decision-making in highly uncertain and competitive environments, which is critical for finance, defense, and resource management. Professionals can develop more adaptive and resilient strategies against unpredictable market shifts or adversarial actions.

How to implement this in your domain

  1. 1Evaluate the ERRL-ZSSDGs framework for developing robust trading algorithms or risk management strategies in volatile markets.
  2. 2Apply the Actor-Critic policy improvement algorithm to model competitive scenarios in your industry, such as pricing wars or supply chain disruptions.
  3. 3Explore how entropy regularization can be used to promote more exploratory and resilient strategies in existing reinforcement learning applications.
  4. 4Develop simulation environments that incorporate regime-switching jump-diffusion processes to test and validate new decision-making models.

Who benefits

BFSIDefenseEnergyLogistics

Key takeaways

  • The ERRL-ZSSDGs framework offers robust strategies for zero-sum games in dynamic environments.
  • It addresses parameter misspecification and sudden environmental changes effectively.
  • Optimal strategies are characterized as probability distributions over actions.
  • An Actor-Critic algorithm approximates solutions for general settings, applicable to investment games.

Original post by Congde Hu, Zhuo Jin, Danping Li, Lin Xu

"arXiv:2606.28669v1 Announce Type: new Abstract: 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 stra…"

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Originally posted by Congde Hu, Zhuo Jin, Danping Li, Lin Xu on X · view source

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