Statistical Limits and Efficient Algorithms for Learning-Enabled Control

As the use of large-scale learning for control continues to grow, the development of sample-efficient algorithms becomes increasingly critical. However, even in the simplest settings, we often do not know algorithms which achieve optimal sample complexity with respect to particular problem instances. This thesis discusses recent progress towards understanding sample efficient algorithms in learning-enabled control. First, we examine tradeoffs between performance and robustness by showing that robust control necessarily sacrifices performance in benign, non-adversarial settings. Next, we examine the problem of offline reinforcement learning over continuous state, action, and observation spaces. We present lower bounds highlighting instances of this problem that have a high sample complexity, regardless of the learning algorithm. We also consider efficient algorithms, and derive the first tight finite sample bounds on the excess cost of learning to control for a general class of nonlinear dynamical systems. Together, these bounds highlight the importance of the dataset, motivating our study of optimal task-oriented experiment design. Finally, we examine the use of large-scale learning for control, in which models trained to perform well on a variety of control tasks are fine-tuned to execute a new control task. We study this problem from the viewpoint of representation learning in the settings of imitation learning and adaptive control, achieving bounds on the imitation gap and regret, respectively.

Author dc:creator

• Lee, Bruce

Advisor dc:contributor.advisor

• Matni, Nikolai

• Electrical Engineering

Language dc:language.iso

en

Repository record dc:identifier.uri

https://repository.upenn.edu/handle/20.500.14332/61672

OAI identifier oai:identifier

oai:repository.upenn.edu:20.500.14332/61672