Learning Lipschitz Feedback Policies from Expert Demonstrations: Closed-Loop Guarantees, Generalization and Robustness

TL;DR

This paper introduces a method to learn feedback control policies from expert demonstrations that guarantees robustness and generalization in closed-loop systems using Lipschitz constraints, with theoretical bounds and empirical validation.

Contribution

It presents a novel Lipschitz-constrained learning framework that provides certified robustness and generalization guarantees for feedback policies learned from demonstrations.

Findings

Finite sample bounds on policy learning error

Guaranteed closed-loop stability under learned policies

Tradeoff between nominal performance and adversarial robustness

Abstract

In this work, we propose a framework to learn feedback control policies with guarantees on closed-loop generalization and adversarial robustness. These policies are learned directly from expert demonstrations, contained in a dataset of state-control input pairs, without any prior knowledge of the task and system model. We use a Lipschitz-constrained loss minimization scheme to learn feedback policies with certified closed-loop robustness, wherein the Lipschitz constraint serves as a mechanism to tune the generalization performance and robustness to adversarial disturbances. Our analysis exploits the Lipschitz property to obtain closed-loop guarantees on generalization and robustness of the learned policies. In particular, we derive a finite sample bound on the policy learning error and establish robust closed-loop stability under the learned control policy. We also derive bounds on the closed-loop regret with respect to the expert policy and the deterioration of closed-loop performance under bounded (adversarial) disturbances to the state measurements. Numerical results validate our analysis and demonstrate the effectiveness of our robust feedback policy learning framework. Finally, our results suggest the existence of a potential tradeoff between nominal closed-loop performance and adversarial robustness, and that improvements in nominal closed-loop performance can only be made at the expense of robustness to adversarial perturbations.