# On the Optimization Landscape of Observer-based Dynamic Linear Quadratic Control

arXiv: https://arxiv.org/abs/2604.10635 · HTML: https://mlsanity.com/paper/2604.10635/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 12 Apr 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 14 of 14)

- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems](https://mlsanity.com/paper/1812.08305/) (2018)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Policy Optimization for H2 Linear Control with H_∞ Robustness Guarantee: Implicit Regularization and Global Convergence](https://mlsanity.com/paper/1910.09496/) (2019)
- [Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem](https://mlsanity.com/paper/1912.11899/) (2019)
- [Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Control](https://mlsanity.com/paper/2102.04393/) (2021)
- [On the Optimization Landscape of Dynamic Output Feedback Linear Quadratic Control](https://mlsanity.com/paper/2201.09598/) (2022)
- [Connectivity of the Feasible and Sublevel Sets of Dynamic Output Feedback Control with Robustness Constraints](https://mlsanity.com/paper/2203.11177/) (2022)
- [On Topological Properties of the Set of Stabilizing Feedback Gains](https://mlsanity.com/paper/1904.08451/) (2019)
- [Globally Convergent Policy Gradient Methods for Linear Quadratic Control of Partially Observed Systems](https://mlsanity.com/paper/2211.04051/) (2022)
- [Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedback](https://mlsanity.com/paper/2310.19022/) (2023)
- [Policy Gradient Methods for Designing Dynamic Output Feedback Controllers](https://mlsanity.com/paper/2210.09735/) (2022)
- [Global Optimality of Single-Timescale Actor-Critic under Continuous State-Action Space: A Study on Linear Quadratic Regulator](https://mlsanity.com/paper/2505.01041/) (2025)
- [Asynchronous Parallel Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/2407.03233/) (2024)

## Abstract (arXiv)

Understanding the optimization landscape of linear quadratic regulation (LQR) problems is fundamental to the design of efficient reinforcement learning solutions. Recent work has made significant progress in characterizing the landscape of static output-feedback control and linear quadratic Gaussian (LQG) control. For LQG, much of the analysis leverages the separation principle, which allows the controller and estimator to be designed independently. However, this simplification breaks down when the gradients with respect to the estimator and controller parameters are inherently coupled, leading to a more intricate analysis. This paper investigates the optimization landscape of observer-based dynamic output-feedback control of LQR problems. We derive the optimal observer-controller pair in settings where transient quadratic performance cannot be neglected. Our analysis reveals that, in general, the combination of the standard LQR controller and the observer that minimizes the trace of the accumulated estimation error covariance does not correspond to a stationary point of the overall closed-loop performance objective. Moreover, we derive a pair of discrete-time Sylvester equations with symmetric structure, both involving the same set of matrix elements, that characterize the stationary point of the observer-based dynamic LQR problem. These equations offer analytical insight into the structure of the optimality conditions and provide a foundation for developing numerical policy gradient methods aimed at learning complex controllers that rely on reconstructed state information.