# Policy Optimization over Submanifolds for Linearly Constrained Feedback Synthesis

arXiv: https://arxiv.org/abs/2201.11157 · HTML: https://mlsanity.com/paper/2201.11157/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2022.

## Built on by (most cited first, 5 of 5)

- [Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies](https://mlsanity.com/paper/2210.04810/) (2022)
- [Online Optimization on Hadamard Manifolds: Curvature Independent Regret Bounds on Horospherically Convex Objectives](https://mlsanity.com/paper/2509.11236/) (2025)
- [Regret Analysis of Policy Optimization over Submanifolds for Linearly Constrained Online LQG](https://mlsanity.com/paper/2403.08553/) (2024)
- [Douglas-Rachford Splitting for Group-Sparse Feedback Linear-Quadratic Control](https://mlsanity.com/paper/2507.19895/) (2025)
- [Curvature-Independent Regret Bounds for Distributed Online Optimization on Hadamard Manifolds](https://mlsanity.com/paper/2609.13646/) (2026)

## Abstract (arXiv)

In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic analysis of a generic constrained smooth cost function, that subsequently facilitates subsuming any such constrained problem into this framework. By studying the second order geometry of this manifold, we provide a Newton-type algorithm that does not rely on the exponential mapping nor a retraction, while ensuring local convergence guarantees. The algorithm hinges instead upon the developed stability certificate and the linear structure of the constraints. We then apply our methodology to two well-known constrained optimal control problems. Finally, several numerical examples showcase the performance of the proposed algorithm.