Model-Agnostic Zeroth-Order Policy Optimization for Meta-Learning of Ergodic Linear Quadratic Regulators

Meta-learning has been proposed as a promising machine learning topic in recent years, with important applications to image classification, robotics, computer games, and control systems. In this paper, we study the problem of using meta-learning to deal with uncertainty and heterogeneity in ergodic linear quadratic regulators. We integrate the zeroth-order optimization technique with a typical meta-learning method, proposing an algorithm that omits the estimation of policy Hessian, which applies to tasks of learning a set of heterogeneous but similar linear dynamic systems. The induced meta-objective function inherits important properties of the original cost function when the set of linear dynamic systems are meta-learnable, allowing the algorithm to optimize over a learnable landscape without projection onto the feasible set. We provide a convergence result for the exact gradient descent process by analyzing the boundedness and smoothness of the gradient for the meta-objective, which justify the proposed algorithm with gradient estimation error being small. We also provide a numerical example to corroborate this perspective.