Riemannian Constrained Policy Optimization via Geometric Stability Certificates∗

Shahriar Talebi, Mehran Mesbahi

Abstract: In this paper, we consider policy optimization over the Riemannian submanifolds of stabilizing controllers arising from constrained Linear Quadratic Regulators (LQR), including output feedback and structured synthesis. In this direction, we provide a Riemannian Newton-type algorithm that enjoys local convergence guarantees and exploits the inherent geometry of the problem. Instead of relying on the exponential mapping or a global retraction, the proposed algorithm revolves around the developed stability certificate and the constraint structure, utilizing the intrinsic geometry of the synthesis problem. We then showcase the utility of the proposed algorithm through numerical examples.