Learning Optimal Controllers for Linear Systems With Multiplicative Noise via Policy Gradient

• 成果类型: Article
• 署名作者: Gravell, Benjamin; Esfahani, Peyman Mohajerin; Summers, Tyler
• 署名单位: University of Texas System; University of Texas Dallas; Delft University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3037046
• 发表日期: 2021
• 页码: 5283-5298
• 关键词: robustness; stability analysis; CONVERGENCE; uncertainty; Covariance matrices; Additive noise; Stochastic processes; gradient methods; noise; optimal control; Reinforcement Learning; Stochastic systems; uncertain systems

摘要

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all recent work in this area, we consider multiplicative noise models, which are increasingly relevant because they explicitly incorporate inherent uncertainty and variation in the system dynamics and thereby improve robustness properties of the controller. Robustness is a critical and poorly understood issue in reinforcement learning; existing methods which do not account for uncertainty can converge to fragile policies or fail to converge at all. Additionally, intentional injection of multiplicative noise into learning algorithms can enhance robustness of policies, as observed in ad hoc work on domain randomization. Although policy gradient algorithms require optimization of a nonconvex cost function, we show that the multiplicative noise LQR cost has a special property called gradient domination, which is exploited to prove global convergence of policy gradient algorithms to the globally optimum control policy with polynomial dependence on problem parameters. Results are provided both in the model-known and model-unknown settings where samples of system trajectories are used to estimate policy gradients