A Moreau Envelope Approach for LQR Meta-Policy Estimation
Ashwin Aravind Mohammad Taha Toghani César A. Uribe
We study the problem of policy estimation for the Linear Quadratic Regulator
(LQR) in discrete-time linear time-invariant uncertain dynamical systems. We
propose a Moreau Envelope-based surrogate LQR cost, built from a finite set of
realizations of the uncertain system, to define a meta-policy efficiently
adjustable to new realizations. Moreover, we design an algorithm to find an
approximate first-order stationary point of the meta-LQR cost function.
Numerical results show that the proposed approach outperforms naive averaging
of controllers on new realizations of the linear system. We also provide
empirical evidence that our method has better sample complexity than
Model-Agnostic Meta-Learning (MAML) approaches.