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

• URL: http://arxiv.org/abs/2405.17370v1
• Date: Mon, 27 May 2024 17:26:36 GMT
• Title: Model-Agnostic Zeroth-Order Policy Optimization for Meta-Learning of Ergodic Linear Quadratic Regulators
• Authors: Yunian Pan, Quanyan Zhu,
• Abstract summary: We study the problem of using meta-learning to deal with uncertainty and heterogeneity in ergodic linear quadratic regulators. We propose an algorithm that omits the estimation of policy Hessian, which applies to tasks of learning a set of heterogeneous but similar linear dynamic systems. We provide a convergence result for the exact gradient descent process by analyzing the boundedness and smoothness of the gradient for the meta-objective.
• Score: 13.343937277604892
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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