# Learning robust control for LQR systems with multiplicative noise via policy gradient

arXiv: https://arxiv.org/abs/1905.13547 · HTML: https://mlsanity.com/paper/1905.13547/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

## Built on by (most cited first, 6 of 6)

- [How are policy gradient methods affected by the limits of control?](https://mlsanity.com/paper/2206.06863/) (2022)
- [Policy Gradient for LQR with Domain Randomization](https://mlsanity.com/paper/2503.24371/) (2025)
- [Review of Metrics to Measure the Stability, Robustness and Resilience of Reinforcement Learning](https://mlsanity.com/paper/2203.12048/) (2022)
- [Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise](https://mlsanity.com/paper/2205.05119/) (2022)
- [Direct Data-Driven Discounted Infinite Horizon Linear Quadratic Regulator with Robustness Guarantees](https://mlsanity.com/paper/2409.10703/) (2024)
- [Global Convergence of Policy Gradient for Entropy Regularized Linear-Quadratic Control with Multiplicative Noise](https://mlsanity.com/paper/2510.02896/) (2025)

## Abstract (arXiv)

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all recent work in this area, we consider multiplicative noise models, which are increasingly relevant because they explicitly incorporate inherent uncertainty and variation in the system dynamics and thereby improve robustness properties of the controller. Robustness is a critical and poorly understood issue in reinforcement learning; existing methods which do not account for uncertainty can converge to fragile policies or fail to converge at all. Additionally, intentional injection of multiplicative noise into learning algorithms can enhance robustness of policies, as observed in ad hoc work on domain randomization. Although policy gradient algorithms require optimization of a non-convex cost function, we show that the multiplicative noise LQR cost has a special property called gradient domination, which is exploited to prove global convergence of policy gradient algorithms to the globally optimum control policy with polynomial dependence on problem parameters. Results are provided both in the model-known and model-unknown settings where samples of system trajectories are used to estimate policy gradients.