# On the Optimization Landscape of Dynamic Output Feedback Linear Quadratic Control

arXiv: https://arxiv.org/abs/2201.09598 · HTML: https://mlsanity.com/paper/2201.09598/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2022.

## Built on by (most cited first, 11 of 11)

- [Distributional Soft Actor-Critic with Three Refinements](https://mlsanity.com/paper/2310.05858/) (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)
- [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)
- [Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedback](https://mlsanity.com/paper/2310.19022/) (2023)
- [Conformal Symplectic Optimization for Stable Reinforcement Learning](https://mlsanity.com/paper/2412.02291/) (2024)
- [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)
- [Optimal Output Feedback Learning Control for Discrete-Time Linear Quadratic Regulation](https://mlsanity.com/paper/2503.06226/) (2025)
- [Actor-Critic Learning for Risk-Constrained Linear Quadratic Regulation](https://mlsanity.com/paper/2510.22267/) (2025)
- [On the Optimization Landscape of Observer-based Dynamic Linear Quadratic Control](https://mlsanity.com/paper/2604.10635/) (2026)

## Abstract (arXiv)

The convergence of policy gradient algorithms hinges on the optimization landscape of the underlying optimal control problem. Theoretical insights into these algorithms can often be acquired from analyzing those of linear quadratic control. However, most of the existing literature only considers the optimization landscape for static full-state or output feedback policies (controllers). We investigate the more challenging case of dynamic output-feedback policies for linear quadratic regulation (abbreviated as dLQR), which is prevalent in practice but has a rather complicated optimization landscape. We first show how the dLQR cost varies with the coordinate transformation of the dynamic controller and then derive the optimal transformation for a given observable stabilizing controller. One of our core results is the uniqueness of the stationary point of dLQR when it is observable, which provides an optimality certificate for solving dynamic controllers using policy gradient methods. Moreover, we establish conditions under which dLQR and linear quadratic Gaussian control are equivalent, thus providing a unified viewpoint of optimal control of both deterministic and stochastic linear systems. These results further shed light on designing policy gradient algorithms for more general decision-making problems with partially observed information.