Reinforcement Learning Method for Zero-Sum Linear-Quadratic Stochastic Differential Games in Infinite Horizons
On the map: Deep reinforcement learning methods → RL for games and combinatorial optimization
Abstract (arXiv)
In this work, we propose, for the first time, a reinforcement learning framework specifically designed for zero-sum linear-quadratic stochastic differential games. This approach offers a generalized solution for scenarios in which accurate system parameters are difficult to obtain, thereby overcoming a key limitation of traditional iterative methods that rely on complete system information. In correspondence with the game-theoretic algebraic Riccati equations associated with the problem, we develop both semi-model-based and model-free reinforcement learning algorithms by combining an iterative solution scheme with dynamic programming principles. Notably, under appropriate rank conditions on data sampling, the convergence of the proposed algorithms is rigorously established through theoretical analysis. Finally, numerical simulations are conducted to verify the effectiveness and feasibility of the proposed method.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods. Builds on 10 of its 34 references that are in the map. First posted on arXiv 8 Feb 2026.
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10 of 34 references.
References · 10
- 2021Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithmscited by 101
- 2020Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Methodcited by 11
- 2021Reinforcement Learning for Adaptive Optimal Stationary Control of Linear Stochastic Systemscited by 8
- 2020Two-Person Zero-Sum Stochastic Linear-Quadratic Differential Gamescited by 3
- 2014Linear Quadratic Stochastic Two-Person Zero-Sum Differential Games in an Infinite Horizoncited by 2
- 2014Linear Quadratic Stochastic Differential Games: Open-Loop and Closed-Loop Saddle Pointscited by 1
- 2022Adaptive dynamic programming-based algorithm for infinite-horizon linear quadratic stochastic optimal control problemscited by 1
- 2023Multidimensional indefinite stochastic Riccati equations and zero-sum stochastic linear-quadratic differential games with non-Markovian regime switchingcited by 1
- 2024Long-Time Behavior of Zero-Sum Linear-Quadratic Stochastic Differential Gamescited by 1
- 2025A Nested Iterative Algorithm for Zero-Sum Linear-Quadratic Stochastic Differential Games in an Infinite Horizoncited by 1
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- 2026Entropy Regularized Reinforcement Learning for Zero-Sum Stochastic Differential Games in a Regime-Switching Jump-Diffusion Process
- 2025Data-Driven Mean Field Equilibrium Computation in Large-Population LQG Games
- 2024Model-free stochastic linear quadratic design by semidefinite programming
- 2026Actor-Dual-Critic Dynamics for Zero-sum and Identical-Interest Stochastic Games
- 2025NashPG: A Policy Gradient Method with Iteratively Refined Regularization for Finding Nash Equilibria
- 2025A non-zero-sum game with reinforcement learning under mean-variance framework