Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914961824940032 |
|---|---|
| author | Pfrommer, Daniel Padmanabhan, Swati Ahn, Kwangjun Umenberger, Jack Marcucci, Tobia Mhammedi, Zakaria Jadbabaie, Ali |
| author_facet | Pfrommer, Daniel Padmanabhan, Swati Ahn, Kwangjun Umenberger, Jack Marcucci, Tobia Mhammedi, Zakaria Jadbabaie, Ali |
| contents | Recent work in imitation learning has shown that having an expert controller that is both suitably smooth and stable enables stronger guarantees on the performance of the learned controller. However, constructing such smoothed expert controllers for arbitrary systems remains challenging, especially in the presence of input and state constraints. As our primary contribution, we show how such a smoothed expert can be designed for a general class of systems using a log-barrier-based relaxation of a standard Model Predictive Control (MPC) optimization problem.
Improving upon our previous work, we show that barrier MPC achieves theoretically optimal error-to-smoothness tradeoff along some direction. At the core of this theoretical guarantee on smoothness is an improved lower bound we prove on the optimality gap of the analytic center associated with a convex Lipschitz function, which we believe could be of independent interest. We validate our theoretical findings via experiments, demonstrating the merits of our smoothing approach over randomized smoothing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control Pfrommer, Daniel Padmanabhan, Swati Ahn, Kwangjun Umenberger, Jack Marcucci, Tobia Mhammedi, Zakaria Jadbabaie, Ali Systems and Control Machine Learning Recent work in imitation learning has shown that having an expert controller that is both suitably smooth and stable enables stronger guarantees on the performance of the learned controller. However, constructing such smoothed expert controllers for arbitrary systems remains challenging, especially in the presence of input and state constraints. As our primary contribution, we show how such a smoothed expert can be designed for a general class of systems using a log-barrier-based relaxation of a standard Model Predictive Control (MPC) optimization problem. Improving upon our previous work, we show that barrier MPC achieves theoretically optimal error-to-smoothness tradeoff along some direction. At the core of this theoretical guarantee on smoothness is an improved lower bound we prove on the optimality gap of the analytic center associated with a convex Lipschitz function, which we believe could be of independent interest. We validate our theoretical findings via experiments, demonstrating the merits of our smoothing approach over randomized smoothing. |
| title | Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control |
| topic | Systems and Control Machine Learning |
| url | https://arxiv.org/abs/2410.00859 |