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Reinforcement learning for exploratory linear-quadratic two-person zero-sum stochastic differential games

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  • Sun, Zhongshi
  • Jia, Guangyan

Abstract

In this paper, we study an entropy-regularized continuous-time linear-quadratic two-person zero-sum stochastic differential game problem from the perspective of reinforcement learning (RL). By the solvability of a discounted algebraic Riccati equation, we construct a Gaussian closed-loop optimal control pair for the problem, which achieves the best tradeoff between exploration and exploitation. Then, in this exploratory framework, we propose an RL algorithm that relies on only partial system information to solve a stochastic H∞ control problem. The corresponding convergence analysis and simulation examples are also provided to verify the efficiency of the proposed algorithm.

Suggested Citation

  • Sun, Zhongshi & Jia, Guangyan, 2023. "Reinforcement learning for exploratory linear-quadratic two-person zero-sum stochastic differential games," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    • Handle: RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322008311
    DOI: 10.1016/j.amc.2022.127763
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    References listed on IDEAS

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    1. Liu, Xikui & Ge, Yingying & Li, Yan, 2019. "Stackelberg games for model-free continuous-time stochastic systems based on adaptive dynamic programming," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    Cited by:

    1. Tian, Xiu-Qin & Liu, Shu-Jun & Yang, Xue, 2024. "Stochastic adaptive linear quadratic nonzero-sum differential games," Applied Mathematics and Computation, Elsevier, vol. 477(C).

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