# Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Control

arXiv: https://arxiv.org/abs/2102.04393 · HTML: https://mlsanity.com/paper/2102.04393/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2021.

## Built on by (most cited first, 28 of 28)

- [Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEs](https://mlsanity.com/paper/2303.10506/) (2023)
- [Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems](https://mlsanity.com/paper/2109.03861/) (2021)
- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [Robot Fleet Learning via Policy Merging](https://mlsanity.com/paper/2310.01362/) (2023)
- [How are policy gradient methods affected by the limits of control?](https://mlsanity.com/paper/2206.06863/) (2022)
- [Revisiting LQR Control from the Perspective of Receding-Horizon Policy Gradient](https://mlsanity.com/paper/2302.13144/) (2023)
- [Learning the Kalman Filter with Fine-Grained Sample Complexity](https://mlsanity.com/paper/2301.12624/) (2023)
- [Global Convergence of Direct Policy Search for State-Feedback H_∞ Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferential](https://mlsanity.com/paper/2210.11577/) (2022)
- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies](https://mlsanity.com/paper/2210.04810/) (2022)
- [Controlgym: Large-Scale Control Environments for Benchmarking Reinforcement Learning Algorithms](https://mlsanity.com/paper/2311.18736/) (2023)
- [Global Convergence of Receding-Horizon Policy Search in Learning Estimator Designs](https://mlsanity.com/paper/2309.04831/) (2023)
- [Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedback](https://mlsanity.com/paper/2310.19022/) (2023)
- [Non-Uniform Noise-to-Signal Ratio in the REINFORCE Policy-Gradient Estimator](https://mlsanity.com/paper/2602.01460/) (2026)
- [Best of Both Worlds Guarantees for Smoothed Online Quadratic Optimization](https://mlsanity.com/paper/2311.00181/) (2023)
- [Mollification Effects of Policy Gradient Methods](https://mlsanity.com/paper/2405.17832/) (2024)
- [On the Optimization Landscape of Dynamic Output Feedback: A Case Study for Linear Quadratic Regulator](https://mlsanity.com/paper/2209.05042/) (2022)
- [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)
- [Model-Free Output Feedback Stabilization via Policy Gradient Methods](https://mlsanity.com/paper/2601.19284/) (2026)
- [Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems](https://mlsanity.com/paper/2602.22577/) (2026)
- [Multitask LQG Control: Performance and Generalization Bounds](https://mlsanity.com/paper/2604.16730/) (2026)
- [Efficient Reinforcement Learning Through Trajectory Generation](https://mlsanity.com/paper/2211.17249/) (2022)
- [Accelerated Optimization Landscape of Linear-Quadratic Regulator](https://mlsanity.com/paper/2307.03590/) (2023)
- [Model-Free μ-Synthesis: A Nonsmooth Optimization Perspective](https://mlsanity.com/paper/2402.11654/) (2024)
- [Principles of frugal inference and control](https://mlsanity.com/paper/2406.14427/) (2024)
- [On the Optimization Landscape of Observer-based Dynamic Linear Quadratic Control](https://mlsanity.com/paper/2604.10635/) (2026)
- [Model-free LQG Control with Chance Constraints](https://mlsanity.com/paper/2605.31310/) (2026)

## Abstract (arXiv)

This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of the optimization landscape of the LQG problem: 1) connectivity of the set of stabilizing controllers Cn; and 2) structure of stationary points. It is known that similarity transformations do not change the input-output behavior of a dynamical controller or LQG cost. This inherent symmetry by similarity transformations makes the landscape of LQG very rich. We show that 1) the set of stabilizing controllers Cn has at most two path-connected components and they are diffeomorphic under a mapping defined by a similarity transformation; 2) there might exist many strictly suboptimal stationary points of the LQG cost function over Cn and these stationary points are always non-minimal; 3) all minimal stationary points are globally optimal and they are identical up to a similarity transformation. These results shed some light on the performance analysis of direct policy gradient methods for solving the LQG problem.