A Moreau Envelope Approach for LQR Meta-Policy Estimation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913535159697408 |
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| author | Aravind, Ashwin Toghani, Mohammad Taha Uribe, César A. |
| author_facet | Aravind, Ashwin Toghani, Mohammad Taha Uribe, César A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_17364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Moreau Envelope Approach for LQR Meta-Policy Estimation Aravind, Ashwin Toghani, Mohammad Taha Uribe, César A. Optimization and Control Machine Learning Systems and Control 49M99, 93E35, 93C05 I.2.8 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. |
| title | A Moreau Envelope Approach for LQR Meta-Policy Estimation |
| topic | Optimization and Control Machine Learning Systems and Control 49M99, 93E35, 93C05 I.2.8 |
| url | https://arxiv.org/abs/2403.17364 |