# On Globally Optimal Stochastic Policy Gradient Methods for Domain Randomized LQR Synthesis

arXiv: https://arxiv.org/abs/2603.14197 · HTML: https://mlsanity.com/paper/2603.14197/

## 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 13 of its 23 references that are in the map.
- First posted on arXiv 15 Mar 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, 13 of 13)

- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [Sim-to-Real Transfer of Robotic Control with Dynamics Randomization](https://mlsanity.com/paper/1710.06537/) (2017)
- [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)
- [Closing the Sim-to-Real Loop: Adapting Simulation Randomization with Real World Experience](https://mlsanity.com/paper/1810.05687/) (2018)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [Deep Drone Racing: From Simulation to Reality with Domain Randomization](https://mlsanity.com/paper/1905.09727/) (2019)
- [Policy Optimization for H2 Linear Control with H_∞ Robustness Guarantee: Implicit Regularization and Global Convergence](https://mlsanity.com/paper/1910.09496/) (2019)
- [LQR through the Lens of First Order Methods: Discrete-time Case](https://mlsanity.com/paper/1907.08921/) (2019)
- [Stabilizing Dynamical Systems via Policy Gradient Methods](https://mlsanity.com/paper/2110.06418/) (2021)
- [Reinforcement learning for non-prehensile manipulation: Transfer from simulation to physical system](https://mlsanity.com/paper/1803.10371/) (2018)
- [Domain Randomization is Sample Efficient for Linear Quadratic Control](https://mlsanity.com/paper/2502.12310/) (2025)
- [Policy Gradient for LQR with Domain Randomization](https://mlsanity.com/paper/2503.24371/) (2025)

## Abstract (arXiv)

Domain randomization is a simple, effective, and flexible scheme for obtaining robust feedback policies aimed at reducing the sim-to-real gap due to model mismatch. While domain randomization methods have yielded impressive demonstrations in the robotics-learning literature, general and theoretically motivated principles for designing optimization schemes that effectively leverage the randomization are largely unexplored. We address this gap by considering a stochastic policy gradient descent method for the domain randomized linear-quadratic regulator synthesis problem, a situation simple enough to provide theoretical guarantees. In particular, we demonstrate that stochastic gradients obtained by repeatedly sampling new systems at each gradient step converge to global optima with appropriate hyperparameters choices, and yield better controllers with lower variability in the final controllers when compared to approaches that do not resample. Sampling is often a quick and cheap operation, so computing policy gradients with newly sampled systems at each iteration is preferable to evaluating gradients on a fixed set of systems.