# Sample Complexity of Linear Quadratic Gaussian (LQG) Control for Output Feedback Systems

arXiv: https://arxiv.org/abs/2011.09929 · HTML: https://mlsanity.com/paper/2011.09929/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2020.

## Built on by (most cited first, 16 of 16)

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- [Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedback](https://mlsanity.com/paper/2310.19022/) (2023)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise](https://mlsanity.com/paper/2205.05119/) (2022)
- [Learning Decentralized Linear Quadratic Regulators with √T Regret](https://mlsanity.com/paper/2210.08886/) (2022)
- [Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control](https://mlsanity.com/paper/2301.07876/) (2023)
- [Policy Evaluation in Distributional LQR](https://mlsanity.com/paper/2303.13657/) (2023)
- [On the Hardness of Learning to Stabilize Linear Systems](https://mlsanity.com/paper/2311.11151/) (2023)
- [Policy Gradient Method for LQG Control via Input-Output-History Representation: Convergence to O(ε)-Stationary Points](https://mlsanity.com/paper/2510.19141/) (2025)
- [Efficient Reinforcement Learning Through Trajectory Generation](https://mlsanity.com/paper/2211.17249/) (2022)

## Abstract (arXiv)

This paper studies a class of partially observed Linear Quadratic Gaussian (LQG) problems with unknown dynamics. We establish an end-to-end sample complexity bound on learning a robust LQG controller for open-loop stable plants. This is achieved using a robust synthesis procedure, where we first estimate a model from a single input-output trajectory of finite length, identify an H-infinity bound on the estimation error, and then design a robust controller using the estimated model and its quantified uncertainty. Our synthesis procedure leverages a recent control tool called Input-Output Parameterization (IOP) that enables robust controller design using convex optimization. For open-loop stable systems, we prove that the LQG performance degrades linearly with respect to the model estimation error using the proposed synthesis procedure. Despite the hidden states in the LQG problem, the achieved scaling matches previous results on learning Linear Quadratic Regulator (LQR) controllers with full state observations.