# Reinforcement Learning Method for Zero-Sum Linear-Quadratic Stochastic Differential Games in Infinite Horizons

arXiv: https://arxiv.org/abs/2602.08075 · HTML: https://mlsanity.com/paper/2602.08075/

## 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.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 10 of 10)

- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Method](https://mlsanity.com/paper/2011.14516/) (2020)
- [Reinforcement Learning for Adaptive Optimal Stationary Control of Linear Stochastic Systems](https://mlsanity.com/paper/2107.07788/) (2021)
- [Two-Person Zero-Sum Stochastic Linear-Quadratic Differential Games](https://mlsanity.com/paper/2005.11701/) (2020)
- [Linear Quadratic Stochastic Two-Person Zero-Sum Differential Games in an Infinite Horizon](https://mlsanity.com/paper/1404.7220/) (2014)
- [Linear Quadratic Stochastic Differential Games: Open-Loop and Closed-Loop Saddle Points](https://mlsanity.com/paper/1401.4754/) (2014)
- [Adaptive dynamic programming-based algorithm for infinite-horizon linear quadratic stochastic optimal control problems](https://mlsanity.com/paper/2210.04486/) (2022)
- [Multidimensional indefinite stochastic Riccati equations and zero-sum stochastic linear-quadratic differential games with non-Markovian regime switching](https://mlsanity.com/paper/2309.05003/) (2023)
- [Long-Time Behavior of Zero-Sum Linear-Quadratic Stochastic Differential Games](https://mlsanity.com/paper/2406.02089/) (2024)
- [A Nested Iterative Algorithm for Zero-Sum Linear-Quadratic Stochastic Differential Games in an Infinite Horizon](https://mlsanity.com/paper/2511.01538/) (2025)

## 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.