Suboptimal Coverings for Continuous Spaces of Control Tasks
Abstract
We propose the α-suboptimal covering number to characterize multi-task control problems where the set of dynamical systems and/or cost functions is infinite, analogous to the cardinality of finite task sets. This notion may help quantify the function class expressiveness needed to represent a good multi-task policy, which is important for learning-based control methods that use parameterized function approximation. We study suboptimal covering numbers for linear dynamical systems with quadratic cost (LQR problems) and construct a class of multi-task LQR problems amenable to analysis. For the scalar case, we show logarithmic dependence on the "breadth" of the space. For the matrix case, we present experiments 1) measuring the efficiency of a particular constructive cover, and 2) visualizing the behavior of two candidate systems for the lower bound.
Cite
Text
Preiss and Sukhatme. "Suboptimal Coverings for Continuous Spaces of Control Tasks." Proceedings of the 3rd Conference on Learning for Dynamics and Control, 2021.Markdown
[Preiss and Sukhatme. "Suboptimal Coverings for Continuous Spaces of Control Tasks." Proceedings of the 3rd Conference on Learning for Dynamics and Control, 2021.](https://mlanthology.org/l4dc/2021/preiss2021l4dc-suboptimal/)BibTeX
@inproceedings{preiss2021l4dc-suboptimal,
title = {{Suboptimal Coverings for Continuous Spaces of Control Tasks}},
author = {Preiss, James A. and Sukhatme, Gaurav S.},
booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control},
year = {2021},
pages = {547-558},
volume = {144},
url = {https://mlanthology.org/l4dc/2021/preiss2021l4dc-suboptimal/}
}