# Robust policy iteration for continuous-time stochastic H_∞ control problem with unknown dynamics

arXiv: https://arxiv.org/abs/2402.04721 · HTML: https://mlsanity.com/paper/2402.04721/

## 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 7 of its 32 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## 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, 7 of 7)

- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [Entropy Regularization for Mean Field Games with Learning](https://mlsanity.com/paper/2010.00145/) (2020)
- [Robust Policy Iteration for Continuous-time Linear Quadratic Regulation](https://mlsanity.com/paper/2005.09528/) (2020)
- [Exploratory LQG Mean Field Games with Entropy Regularization](https://mlsanity.com/paper/2011.12946/) (2020)
- [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)
- [Linear Quadratic Stochastic Two-Person Zero-Sum Differential Games in an Infinite Horizon](https://mlsanity.com/paper/1404.7220/) (2014)

## Abstract (arXiv)

In this article, we study a continuous-time stochastic H_∞ control problem based on reinforcement learning (RL) techniques that can be viewed as solving a stochastic linear-quadratic two-person zero-sum differential game (LQZSG). First, we propose an RL algorithm that can iteratively solve stochastic game algebraic Riccati equation based on collected state and control data when all dynamic system information is unknown. In addition, the algorithm only needs to collect data once during the iteration process. Then, we discuss the robustness and convergence of the inner and outer loops of the policy iteration algorithm, respectively, and show that when the error of each iteration is within a certain range, the algorithm can converge to a small neighborhood of the saddle point of the stochastic LQZSG problem. Finally, we applied the proposed RL algorithm to two simulation examples to verify the effectiveness of the algorithm.