Extended Convex Lifting for Policy Optimization of Optimal and Robust Control

Yang Zheng, Chih-Fan Pai, Yujie Tang
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:392-404, 2025.

Abstract

Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In this paper, we introduce the Extended Convex Lifting (ECL) framework, which reveals hidden convexity in classical optimal and robust control problems from a modern optimization perspective. Our ECL framework offers a bridge between nonconvex policy optimization and convex reformulations. Despite non-convexity and non-smoothness, the existence of an ECL for policy optimization not only reveals that the policy optimization problem is equivalent to a convex problem, but also certifies a class of first-order non-degenerate stationary points to be globally optimal. We further show that this ECL framework encompasses many benchmark control problems, including LQR, state-feedback and output-feedback H-infinity robust control. We believe that ECL will also be of independent interest for analyzing nonconvex problems beyond control.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-zheng25a, title = {Extended Convex Lifting for Policy Optimization of Optimal and Robust Control}, author = {Zheng, Yang and Pai, Chih-Fan and Tang, Yujie}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {392--404}, 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/zheng25a/zheng25a.pdf}, url = {https://proceedings.mlr.press/v283/zheng25a.html}, abstract = {Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In this paper, we introduce the Extended Convex Lifting (ECL) framework, which reveals hidden convexity in classical optimal and robust control problems from a modern optimization perspective. Our ECL framework offers a bridge between nonconvex policy optimization and convex reformulations. Despite non-convexity and non-smoothness, the existence of an ECL for policy optimization not only reveals that the policy optimization problem is equivalent to a convex problem, but also certifies a class of first-order non-degenerate stationary points to be globally optimal. We further show that this ECL framework encompasses many benchmark control problems, including LQR, state-feedback and output-feedback H-infinity robust control. We believe that ECL will also be of independent interest for analyzing nonconvex problems beyond control.} }
Endnote
%0 Conference Paper %T Extended Convex Lifting for Policy Optimization of Optimal and Robust Control %A Yang Zheng %A Chih-Fan Pai %A Yujie Tang %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-zheng25a %I PMLR %P 392--404 %U https://proceedings.mlr.press/v283/zheng25a.html %V 283 %X Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In this paper, we introduce the Extended Convex Lifting (ECL) framework, which reveals hidden convexity in classical optimal and robust control problems from a modern optimization perspective. Our ECL framework offers a bridge between nonconvex policy optimization and convex reformulations. Despite non-convexity and non-smoothness, the existence of an ECL for policy optimization not only reveals that the policy optimization problem is equivalent to a convex problem, but also certifies a class of first-order non-degenerate stationary points to be globally optimal. We further show that this ECL framework encompasses many benchmark control problems, including LQR, state-feedback and output-feedback H-infinity robust control. We believe that ECL will also be of independent interest for analyzing nonconvex problems beyond control.
APA
Zheng, Y., Pai, C. & Tang, Y.. (2025). Extended Convex Lifting for Policy Optimization of Optimal and Robust Control. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:392-404 Available from https://proceedings.mlr.press/v283/zheng25a.html.

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