Globally Convergent Policy Gradient Methods for Linear Quadratic Control of Partially Observed Systems

Abstract: While the optimization landscape of policy gradient methods has been recently investigated for partially observed linear systems in terms of both static output feedback and dynamical controllers, they only provide convergence guarantees to stationary points. In this paper, we propose a new policy parameterization for partially observed linear systems, using a past input-output trajectory of finite length as feedback. We show that the solution set to the parameterized optimization problem is a matrix space, which is invariant to similarity transformation. By proving a gradient dominance property, we show the global convergence of policy gradient methods. Moreover, we observe that the gradient is orthogonal to the solution set, revealing an explicit relation between the resulting solution and the initial policy. Finally, we perform simulations to validate our theoretical results.