# Reinforcement Learning for a Discrete-Time Linear-Quadratic Control Problem with an Application

arXiv: https://arxiv.org/abs/2412.05906 · HTML: https://mlsanity.com/paper/2412.05906/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 3 of its 11 references that are in the map.
- First posted on arXiv 8 Dec 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 3 of 3)

- [Reinforcement Learning in Healthcare: A Survey](https://mlsanity.com/paper/1908.08796/) (2019)
- [Regret Analysis of Learning-Based MPC with Partially-Unknown Cost Function](https://mlsanity.com/paper/2108.02307/) (2021)
- [Discrete-Time Mean-Variance Strategy Based on Reinforcement Learning](https://mlsanity.com/paper/2312.15385/) (2023)

## Abstract (arXiv)

We study the discrete-time linear-quadratic (LQ) control model using reinforcement learning (RL). Using entropy to measure the cost of exploration, we prove that the optimal feedback policy for the problem must be Gaussian type. Then, we apply the results of the discrete-time LQ model to solve the discrete-time mean-variance asset-liability management problem and prove our RL algorithm's policy improvement and convergence. Finally, a numerical example sheds light on the theoretical results established using simulations.