# Stochastic Linear Quadratic Optimal Control Problem: A Reinforcement Learning Method

arXiv: https://arxiv.org/abs/2011.14516 · HTML: https://mlsanity.com/paper/2011.14516/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 11 of 11)

- [Mean Field LQG Social Optimization: A Reinforcement Learning Approach](https://mlsanity.com/paper/2410.15119/) (2024)
- [Inverse reinforcement learning by expert imitation for the stochastic linear-quadratic optimal control problem](https://mlsanity.com/paper/2405.17085/) (2024)
- [Robust Mean Field Social Control: A Unified Reinforcement Learning Framework](https://mlsanity.com/paper/2502.20029/) (2025)
- [Robust policy iteration for continuous-time stochastic H_∞ control problem with unknown dynamics](https://mlsanity.com/paper/2402.04721/) (2024)
- [Convergence of Policy Gradient for Stochastic Linear-Quadratic Control Problem in Infinite Horizon](https://mlsanity.com/paper/2404.11382/) (2024)
- [Heavy-Ball Momentum Accelerated Actor-Critic With Function Approximation](https://mlsanity.com/paper/2408.06945/) (2024)
- [Two Kinds of Learning Algorithms for Continuous-Time VWAP Targeting Execution](https://mlsanity.com/paper/2411.06645/) (2024)
- [Global Convergence of Policy Gradient for Entropy Regularized Linear-Quadratic Control with Multiplicative Noise](https://mlsanity.com/paper/2510.02896/) (2025)
- [Reinforcement Learning Method for Zero-Sum Linear-Quadratic Stochastic Differential Games in Infinite Horizons](https://mlsanity.com/paper/2602.08075/) (2026)
- [Data-Driven Network LQG Mean Field Games with Heterogeneous Populations via Integral Reinforcement Learning](https://mlsanity.com/paper/2602.14339/) (2026)
- [Stabilizer Design for Policy Iteration in Stochastic Linear Quadratic Control: A Spectrum-Assignment Approach](https://mlsanity.com/paper/2608.05953/) (2026)

## Abstract (arXiv)

This paper applies a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where drift and diffusion terms in the dynamics may depend on both the state and control. Based on Bellman's dynamic programming principle, an online RL algorithm is presented to attain the optimal control with just partial system information. This algorithm directly computes the optimal control rather than estimating the system coefficients and solving the related Riccati equation. It just requires local trajectory information, greatly simplifying the calculation processing. Two numerical examples are carried out to shed light on our theoretical findings.