Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929368902664192 |
|---|---|
| author | Toso, Leonardo F. Zhan, Donglin Anderson, James Wang, Han |
| author_facet | Toso, Leonardo F. Zhan, Donglin Anderson, James Wang, Han |
| contents | We investigate the problem of learning linear quadratic regulators (LQR) in a multi-task, heterogeneous, and model-free setting. We characterize the stability and personalization guarantees of a policy gradient-based (PG) model-agnostic meta-learning (MAML) (Finn et al., 2017) approach for the LQR problem under different task-heterogeneity settings. We show that our MAML-LQR algorithm produces a stabilizing controller close to each task-specific optimal controller up to a task-heterogeneity bias in both model-based and model-free learning scenarios. Moreover, in the model-based setting, we show that such a controller is achieved with a linear convergence rate, which improves upon sub-linear rates from existing work. Our theoretical guarantees demonstrate that the learned controller can efficiently adapt to unseen LQR tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR Toso, Leonardo F. Zhan, Donglin Anderson, James Wang, Han Optimization and Control Machine Learning We investigate the problem of learning linear quadratic regulators (LQR) in a multi-task, heterogeneous, and model-free setting. We characterize the stability and personalization guarantees of a policy gradient-based (PG) model-agnostic meta-learning (MAML) (Finn et al., 2017) approach for the LQR problem under different task-heterogeneity settings. We show that our MAML-LQR algorithm produces a stabilizing controller close to each task-specific optimal controller up to a task-heterogeneity bias in both model-based and model-free learning scenarios. Moreover, in the model-based setting, we show that such a controller is achieved with a linear convergence rate, which improves upon sub-linear rates from existing work. Our theoretical guarantees demonstrate that the learned controller can efficiently adapt to unseen LQR tasks. |
| title | Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2401.14534 |