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

arXiv: https://arxiv.org/abs/2103.16629 · HTML: https://mlsanity.com/paper/2103.16629/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 30 Mar 2021.

## Builds on (most cited first, 21 of 21)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Discriminator-Actor-Critic: Addressing Sample Inefficiency and Reward Bias in Adversarial Imitation Learning](https://mlsanity.com/paper/1809.02925/) (2018)
- [DART: Noise Injection for Robust Imitation Learning](https://mlsanity.com/paper/1703.09327/) (2017)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators](https://mlsanity.com/paper/1903.01014/) (2019)
- [Model-Free Imitation Learning with Policy Optimization](https://mlsanity.com/paper/1605.08478/) (2016)
- [Task-Relevant Adversarial Imitation Learning](https://mlsanity.com/paper/1910.01077/) (2019)
- [On the Sample Complexity of Stability Constrained Imitation Learning](https://mlsanity.com/paper/2102.09161/) (2021)
- [Stability-certified reinforcement learning: A control-theoretic perspective](https://mlsanity.com/paper/1810.11505/) (2018)
- [CLIP: Cheap Lipschitz Training of Neural Networks](https://mlsanity.com/paper/2103.12531/) (2021)
- [Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constant](https://mlsanity.com/paper/2001.06263/) (2020)
- [Robust Guarantees for Perception-Based Control](https://mlsanity.com/paper/1907.03680/) (2019)
- [Lipschitz Bounds and Provably Robust Training by Laplacian Smoothing](https://mlsanity.com/paper/2006.03712/) (2020)
- [Convergence Properties for Discrete-time Nonlinear Systems](https://mlsanity.com/paper/1612.05327/) (2016)
- [Accuracy Prevents Robustness in Perception-based Control](https://mlsanity.com/paper/1910.00119/) (2019)
- [On the Robustness of Data-Driven Controllers for Linear Systems](https://mlsanity.com/paper/1912.10231/) (2019)

## Abstract (arXiv)

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.