mlsanityData to 14 Oct 2026

Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems

arXiv 2602.22577 ↗First posted 26 Feb 2026math.OC cs.SY eess.SYcited by 1

On the map: Deep reinforcement learning methods → RL for games and combinatorial optimization

Abstract (arXiv)

Despite its nonconvexity, policy optimization for the Linear Quadratic Regulator (LQR) admits a favorable structural property known as gradient dominance, which facilitates linear convergence of policy gradient methods to the globally optimal gain. While gradient dominance has been extensively studied, continuous-time and discrete-time LQRs have largely been analyzed separately, relying on slightly different assumptions, proof strategies, and resulting guarantees. In this paper, we present a unified gradient dominance property for both continuous-time and discrete-time LQRs under mild stabilizability and detectability assumptions. Our analysis is based on a convex reformulation derived from a common Lyapunov inequality representation and a unified change-of-variables procedure. This convex-lifting perspective yields a single proof framework applicable to both time models. The unified treatment clarifies how differences between continuous-time and discrete-time dynamics influence theoretical guarantees and reveals a deeper structural symmetry between the two formulations. Numerical examples illustrate and support the theoretical findings.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods. Builds on 23 of its 40 references that are in the map. First posted on arXiv 26 Feb 2026.

Builds on

23 of 40 references.

Closest ancestors · 1

Same direction, newest first

  1. 2025Policy Gradient for LQR with Domain Randomization31 Mar

Other references · 22

  1. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 539
  2. 2018Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulatorcited by 250
  3. 2019LQR through the Lens of First Order Methods: Discrete-time Casecited by 40
  4. 2021Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Controlcited by 28
  5. 2020Optimizing Static Linear Feedback: Gradient Methodcited by 27
  6. 2019Learning the Globally Optimal Distributed LQ Regulatorcited by 20
  7. 2020Policy Gradient-based Algorithms for Continuous-time Linear Quadratic Controlcited by 13
  8. 2023Stochastic Optimization under Hidden Convexitycited by 12
  9. 2024Data-Enabled Policy Optimization for Direct Adaptive Learning of the LQRcited by 9
  10. 2022Global Convergence of Direct Policy Search for State-Feedback H_∞ Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferentialcited by 7
  11. 2023Error bounds, PL condition, and quadratic growth for weakly convex functions, and linear convergences of proximal point methodscited by 7
  12. 2022Escaping High-order Saddles in Policy Optimization for Linear Quadratic Gaussian (LQG) Controlcited by 5
10 more
  1. 2025Model-free Online Learning for the Kalman Filter: Forgetting Factor and Logarithmic Regretcited by 4
  2. 2023Benign Nonconvex Landscapes in Optimal and Robust Control, Part I: Global Optimalitycited by 3
  3. 2024Convergence Analysis of Gradient Flow for Overparameterized LQR Formulationscited by 3
  4. 2025Revisiting Strong Duality, Hidden Convexity, and Gradient Dominance in the Linear Quadratic Regulatorcited by 3
  5. 2024Policy Optimization in Control: Geometry and Algorithmic Implicationscited by 2
  6. 2025Policy Optimization in Robust Control: Weak Convexity and Subgradient Methodscited by 2
  7. 2024Benign Nonconvex Landscapes in Optimal and Robust Control, Part II: Extended Convex Liftingcited by 1
  8. 2025Remarks on the Polyak-Lojasiewicz inequality and the convergence of gradient systemscited by 1
  9. 2025Semidefinite Programming Duality in Infinite-Horizon Linear Quadratic Differential Gamescited by 1
  10. 2025Policy Optimization in the Linear Quadratic Gaussian Problem: A Frequency Domain Perspectivecited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Model-free LQG Control with Chance Constraintscited by 0

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  1. 2025On the Gradient Domination of the LQG Problem
  2. 2026On the Optimization Landscape of Observer-based Dynamic Linear Quadratic Control
  3. 2025Second-Order Policy Gradient Methods for the Linear Quadratic Regulator
  4. 2024Sample Complexity of the Linear Quadratic Regulator: A Reinforcement Learning Lens
  5. 2025Bridging Continuous-time LQR and Reinforcement Learning via Gradient Flow of the Bellman Error
  6. 2026Data-Driven Continuous-Time Linear Quadratic Regulator via Closed-Loop and Reinforcement Learning Parameterizations
  7. 2026Global Convergence of Policy Gradient Methods for ReLU Controllers in Linear Quadratic Regulation
  8. 2025On the Robustness of Derivative-free Methods for Linear Quadratic Regulator