Domain Randomization is Sample Efficient for Linear Quadratic Control

Tesshu Fujinami, Bruce D. Lee, Nikolai Matni, George J. Pappas
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:907-919, 2025.

Abstract

We study the sample efficiency of domain randomization and robust control for the benchmark problem of learning the linear quadratic regulator (LQR). Domain randomization, which synthesizes controllers by minimizing average performance over a distribution of model parameters, has achieved empirical success in robotics, but its theoretical properties remain poorly understood. We establish that with an appropriately chosen sampling distribution, domain randomization achieves the optimal asymptotic rate of decay in the excess cost, matching certainty equivalence. We further demonstrate that robust control, while potentially overly conservative, exhibits superior performance in the low-data regime due to its ability to stabilize uncertain systems with coarse parameter estimates. We propose a gradient-based algorithm for domain randomization that performs well in numerical experiments, which enables us to validate the trends predicted by our analysis. These results provide insights into the use of domain randomization in learning-enabled control, and highlight several open questions about its application to broader classes of systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-fujinami25a, title = {Domain Randomization is Sample Efficient for Linear Quadratic Control}, author = {Fujinami, Tesshu and Lee, Bruce D. and Matni, Nikolai and Pappas, George J.}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {907--919}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/fujinami25a/fujinami25a.pdf}, url = {https://proceedings.mlr.press/v283/fujinami25a.html}, abstract = {We study the sample efficiency of domain randomization and robust control for the benchmark problem of learning the linear quadratic regulator (LQR). Domain randomization, which synthesizes controllers by minimizing average performance over a distribution of model parameters, has achieved empirical success in robotics, but its theoretical properties remain poorly understood. We establish that with an appropriately chosen sampling distribution, domain randomization achieves the optimal asymptotic rate of decay in the excess cost, matching certainty equivalence. We further demonstrate that robust control, while potentially overly conservative, exhibits superior performance in the low-data regime due to its ability to stabilize uncertain systems with coarse parameter estimates. We propose a gradient-based algorithm for domain randomization that performs well in numerical experiments, which enables us to validate the trends predicted by our analysis. These results provide insights into the use of domain randomization in learning-enabled control, and highlight several open questions about its application to broader classes of systems.} }
Endnote
%0 Conference Paper %T Domain Randomization is Sample Efficient for Linear Quadratic Control %A Tesshu Fujinami %A Bruce D. Lee %A Nikolai Matni %A George J. Pappas %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-fujinami25a %I PMLR %P 907--919 %U https://proceedings.mlr.press/v283/fujinami25a.html %V 283 %X We study the sample efficiency of domain randomization and robust control for the benchmark problem of learning the linear quadratic regulator (LQR). Domain randomization, which synthesizes controllers by minimizing average performance over a distribution of model parameters, has achieved empirical success in robotics, but its theoretical properties remain poorly understood. We establish that with an appropriately chosen sampling distribution, domain randomization achieves the optimal asymptotic rate of decay in the excess cost, matching certainty equivalence. We further demonstrate that robust control, while potentially overly conservative, exhibits superior performance in the low-data regime due to its ability to stabilize uncertain systems with coarse parameter estimates. We propose a gradient-based algorithm for domain randomization that performs well in numerical experiments, which enables us to validate the trends predicted by our analysis. These results provide insights into the use of domain randomization in learning-enabled control, and highlight several open questions about its application to broader classes of systems.
APA
Fujinami, T., Lee, B.D., Matni, N. & Pappas, G.J.. (2025). Domain Randomization is Sample Efficient for Linear Quadratic Control. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:907-919 Available from https://proceedings.mlr.press/v283/fujinami25a.html.

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