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

arXiv: https://arxiv.org/abs/2602.22577 · HTML: https://mlsanity.com/paper/2602.22577/

## Key facts

- Cited by 1 papers 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.

## 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, 23 of 23)

- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [LQR through the Lens of First Order Methods: Discrete-time Case](https://mlsanity.com/paper/1907.08921/) (2019)
- [Analysis of the Optimization Landscape of Linear Quadratic Gaussian (LQG) Control](https://mlsanity.com/paper/2102.04393/) (2021)
- [Optimizing Static Linear Feedback: Gradient Method](https://mlsanity.com/paper/2004.09875/) (2020)
- [Learning the Globally Optimal Distributed LQ Regulator](https://mlsanity.com/paper/1912.08774/) (2019)
- [Policy Gradient-based Algorithms for Continuous-time Linear Quadratic Control](https://mlsanity.com/paper/2006.09178/) (2020)
- [Stochastic Optimization under Hidden Convexity](https://mlsanity.com/paper/2401.00108/) (2023)
- [Data-Enabled Policy Optimization for Direct Adaptive Learning of the LQR](https://mlsanity.com/paper/2401.14871/) (2024)
- [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)
- [Error bounds, PL condition, and quadratic growth for weakly convex functions, and linear convergences of proximal point methods](https://mlsanity.com/paper/2312.16775/) (2023)
- [Escaping High-order Saddles in Policy Optimization for Linear Quadratic Gaussian (LQG) Control](https://mlsanity.com/paper/2204.00912/) (2022)
- [Policy Gradient for LQR with Domain Randomization](https://mlsanity.com/paper/2503.24371/) (2025)
- [Model-free Online Learning for the Kalman Filter: Forgetting Factor and Logarithmic Regret](https://mlsanity.com/paper/2505.08982/) (2025)
- [Benign Nonconvex Landscapes in Optimal and Robust Control, Part I: Global Optimality](https://mlsanity.com/paper/2312.15332/) (2023)
- [Convergence Analysis of Gradient Flow for Overparameterized LQR Formulations](https://mlsanity.com/paper/2408.15456/) (2024)
- [Revisiting Strong Duality, Hidden Convexity, and Gradient Dominance in the Linear Quadratic Regulator](https://mlsanity.com/paper/2503.10964/) (2025)
- [Policy Optimization in Control: Geometry and Algorithmic Implications](https://mlsanity.com/paper/2406.04243/) (2024)
- [Policy Optimization in Robust Control: Weak Convexity and Subgradient Methods](https://mlsanity.com/paper/2509.25633/) (2025)
- [Benign Nonconvex Landscapes in Optimal and Robust Control, Part II: Extended Convex Lifting](https://mlsanity.com/paper/2406.04001/) (2024)
- [Remarks on the Polyak-Lojasiewicz inequality and the convergence of gradient systems](https://mlsanity.com/paper/2503.23641/) (2025)
- [Semidefinite Programming Duality in Infinite-Horizon Linear Quadratic Differential Games](https://mlsanity.com/paper/2504.02201/) (2025)
- [Policy Optimization in the Linear Quadratic Gaussian Problem: A Frequency Domain Perspective](https://mlsanity.com/paper/2508.17252/) (2025)

## Built on by (most cited first, 1 of 1)

- [Model-free LQG Control with Chance Constraints](https://mlsanity.com/paper/2605.31310/) (2026)

## 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.