Policy Optimization for Markovian Jump Linear Quadratic Control: Gradient-Based Methods and Global Convergence
arXiv:2011.11852
Abstract
Recently, policy optimization for control purposes has received renewed attention due to the increasing interest in reinforcement learning. In this paper, we investigate the global convergence of gradient-based policy optimization methods for quadratic optimal control of discrete-time Markovian jump linear systems (MJLS). First, we study the optimization landscape of direct policy optimization for MJLS, with static state feedback controllers and quadratic performance costs. Despite the non-convexity of the resultant problem, we are still able to identify several useful properties such as coercivity, gradient dominance, and almost smoothness. Based on these properties, we show global convergence of three types of policy optimization methods: the gradient descent method; the Gauss-Newton method; and the natural policy gradient method. We prove that all three methods converge to the optimal state feedback controller for MJLS at a linear rate if initialized at a controller which is mean-square stabilizing. Some numerical examples are presented to support the theory. This work brings new insights for understanding the performance of policy gradient methods on the Markovian jump linear quadratic control problem.
References in corpus (7)
- Trust Region Policy Optimization
- Deep Reinforcement Learning that Matters
- Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator
- Bayesian Nonparametric Inference of Switching Linear Dynamical Systems
- LQR through the Lens of First Order Methods: Discrete-time Case
- On the Global Convergence of Actor-Critic: A Case for Linear Quadratic Regulator with Ergodic Cost
- Combining Model-Based and Model-Free Methods for Nonlinear Control: A Provably Convergent Policy Gradient Approach