# Robust Reinforcement Learning for Risk-Sensitive Linear Quadratic Gaussian Control

arXiv: https://arxiv.org/abs/2212.02072 · HTML: https://mlsanity.com/paper/2212.02072/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2022.

## Built on by (most cited first, 7 of 7)

- [Global Convergence of Receding-Horizon Policy Search in Learning Estimator Designs](https://mlsanity.com/paper/2309.04831/) (2023)
- [Robust Mean Field Social Control: A Unified Reinforcement Learning Framework](https://mlsanity.com/paper/2502.20029/) (2025)
- [On the Robustness of Derivative-free Methods for Linear Quadratic Regulator](https://mlsanity.com/paper/2506.12596/) (2025)
- [Actor-Critic Learning for Risk-Constrained Linear Quadratic Regulation](https://mlsanity.com/paper/2510.22267/) (2025)
- [Comparative Study of Q-Learning for State-Feedback LQG Control with an Unknown Model](https://mlsanity.com/paper/2511.07870/) (2025)
- [Stabilizer Design for Policy Iteration in Stochastic Linear Quadratic Control: A Spectrum-Assignment Approach](https://mlsanity.com/paper/2608.05953/) (2026)
- [Decentralized Strategies for Finite Population LQG Social Control: A Reinforcement Learning Approach](https://mlsanity.com/paper/2608.30244/) (2026)

## Abstract (arXiv)

This paper proposes a novel robust reinforcement learning framework for discrete-time linear systems with model mismatch that may arise from the sim-to-real gap. A key strategy is to invoke advanced techniques from control theory. Using the formulation of the classical risk-sensitive linear quadratic Gaussian control, a dual-loop policy optimization algorithm is proposed to generate a robust optimal controller. The dual-loop policy optimization algorithm is shown to be globally and uniformly convergent, and robust against disturbances during the learning process. This robustness property is called small-disturbance input-to-state stability and guarantees that the proposed policy optimization algorithm converges to a small neighborhood of the optimal controller as long as the disturbance at each learning step is relatively small. In addition, when the system dynamics is unknown, a novel model-free off-policy policy optimization algorithm is proposed. Finally, numerical examples are provided to illustrate the proposed algorithm.