# Policy Gradient Methods for Discrete Time Linear Quadratic Regulator With Random Parameters

arXiv: https://arxiv.org/abs/2303.16548 · HTML: https://mlsanity.com/paper/2303.16548/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 19 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 7 of 7)

- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Policy Gradient Methods for the Noisy Linear Quadratic Regulator over a Finite Horizon](https://mlsanity.com/paper/2011.10300/) (2020)
- [The Gap Between Model-Based and Model-Free Methods on the Linear Quadratic Regulator: An Asymptotic Viewpoint](https://mlsanity.com/paper/1812.03565/) (2018)
- [Model-free optimal control of discrete-time systems with additive and multiplicative noises](https://mlsanity.com/paper/2008.08734/) (2020)
- [A Q-learning algorithm for discrete-time linear-quadratic control with random parameters of unknown distribution: convergence and stabilization](https://mlsanity.com/paper/2011.04970/) (2020)

## Abstract (arXiv)

This paper studies an infinite horizon optimal control problem for discrete-time linear system and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. In this general setting, we apply the policy gradient method, a reinforcement learning technique, to search for the optimal control without requiring knowledge of statistical information of the parameters. We investigate the sub-Gaussianity of the state process and establish global linear convergence guarantee for this approach based on assumptions that are weaker and easier to verify compared to existing results. Numerical experiments are presented to illustrate our result.