mlsanityData to 7 Oct 2026

Optimizing Static Linear Feedback: Gradient Method

arXiv 2004.09875 ↗First posted 21 Apr 2020math.OCcited by 19

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Abstract (arXiv)

The linear quadratic regulator is the fundamental problem of optimal control. Its state feedback version was set and solved in the early 1960s. However the static output feedback problem has no explicit-form solution. It is suggested to look at both of them from another point of view as matrix optimization problems, where the variable is a feedback matrix gain. The properties of such a function are investigated, it turns out to be smooth, but not convex, with possible non-connected domain. Nevertheless, the gradient method for it with the special step-size choice converges to the optimal solution in the state feedback case and to a stationary point in the output feedback case. The results can be extended for the general framework of unconstrained optimization and for reduced gradient method for minimization with equality-type constraints.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Apr 2020.

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Citing papers per year: 2021: 2; 2022: 4; 2023: 5; 2024: 4; 2025: 2; 2026: 2.

19 papers.

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  1. 2023Stochastic Policy Gradient Methods: Improved Sample Complexity for Fisher-non-degenerate Policiescited by 53
  2. 2021Derivative-Free Policy Optimization for Linear Risk-Sensitive and Robust Control Design: Implicit Regularization and Sample Complexitycited by 15
  3. 2024Taming Nonconvex Stochastic Mirror Descent with General Bregman Divergencecited by 11
  4. 2022Towards a Theoretical Foundation of Policy Optimization for Learning Control Policiescited by 6
  5. 2022Global Convergence of Direct Policy Search for State-Feedback H_∞ Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferentialcited by 6
  6. 2021Model-Free μ Synthesis via Adversarial Reinforcement Learningcited by 5
  7. 2022From Gradient Flow on Population Loss to Learning with Stochastic Gradient Descentcited by 5
  8. 2023Connected Superlevel Set in (Deep) Reinforcement Learning and its Application to Minimax Theoremscited by 3
  9. 2023Learning Zero-Sum Linear Quadratic Games with Improved Sample Complexity and Last-Iterate Convergencecited by 3
  10. 2023Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedbackcited by 2
  11. 2024On the Complexity of Finite-Sum Smooth Optimization under the Polyak-Lojasiewicz Conditioncited by 2
  12. 2022On the Optimization Landscape of Dynamic Output Feedback: A Case Study for Linear Quadratic Regulatorcited by 1
7 more
  1. 2024Model-Free Learning for the Linear Quadratic Regulator over Rate-Limited Channelscited by 1
  2. 2023Accelerated Optimization Landscape of Linear-Quadratic Regulatorcited by 0
  3. 2024Model-Free μ-Synthesis: A Nonsmooth Optimization Perspectivecited by 0
  4. 2025Remarks on the Polyak-Lojasiewicz inequality and the convergence of gradient systemscited by 0
  5. 2025Some remarks on gradient dominance and LQR policy optimizationcited by 0
  6. 2026Model-Free Output Feedback Stabilization via Policy Gradient Methodscited by 0
  7. 2026Learning Suffers More Than the Policy Class Under Partial Observability: A Closed-Form Analysiscited by 0