Model-Agnostic Zeroth-Order Policy Optimization for Meta-Learning of Ergodic Linear Quadratic Regulators
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913365118418944 |
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| author | Pan, Yunian Zhu, Quanyan |
| author_facet | Pan, Yunian Zhu, Quanyan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_17370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Model-Agnostic Zeroth-Order Policy Optimization for Meta-Learning of Ergodic Linear Quadratic Regulators Pan, Yunian Zhu, Quanyan Systems and Control Machine Learning 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. |
| title | Model-Agnostic Zeroth-Order Policy Optimization for Meta-Learning of Ergodic Linear Quadratic Regulators |
| topic | Systems and Control Machine Learning |
| url | https://arxiv.org/abs/2405.17370 |