# Robust Behavior Cloning Via Global Lipschitz Regularization

arXiv: https://arxiv.org/abs/2506.19250 · HTML: https://mlsanity.com/paper/2506.19250/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 13 of 13)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [BC-Z: Zero-Shot Task Generalization with Robotic Imitation Learning](https://mlsanity.com/paper/2202.02005/) (2022)
- [Exploring the Limitations of Behavior Cloning for Autonomous Driving](https://mlsanity.com/paper/1904.08980/) (2019)
- [Robust Deep Reinforcement Learning against Adversarial Perturbations on State Observations](https://mlsanity.com/paper/2003.08938/) (2020)
- [Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspective](https://mlsanity.com/paper/2210.01787/) (2022)
- [Policy Smoothing for Provably Robust Reinforcement Learning](https://mlsanity.com/paper/2106.11420/) (2021)
- [Improve Robustness of Reinforcement Learning against Observation Perturbations via l_∞ Lipschitz Policy Networks](https://mlsanity.com/paper/2312.08751/) (2023)
- [A Survey of Deep Network Solutions for Learning Control in Robotics: From Reinforcement to Imitation](https://mlsanity.com/paper/1612.07139/) (2016)
- [Tight Performance Guarantees of Imitator Policies with Continuous Actions](https://mlsanity.com/paper/2212.03922/) (2022)
- [Certifying Model Accuracy under Distribution Shifts](https://mlsanity.com/paper/2201.12440/) (2022)
- [Adversarially Regularized Policy Learning Guided by Trajectory Optimization](https://mlsanity.com/paper/2109.07627/) (2021)

## Built on by (most cited first, 2 of 2)

- [Balance Equation-based Distributionally Robust Offline Imitation Learning](https://mlsanity.com/paper/2511.07942/) (2025)
- [When Dynamics Shift, Robust Task Inference Wins: Offline Imitation Learning with Behavior Foundation Models Revisited](https://mlsanity.com/paper/2605.17017/) (2026)

## Abstract (arXiv)

Behavior Cloning (BC) is an effective imitation learning technique and has even been adopted in some safety-critical domains such as autonomous vehicles. BC trains a policy to mimic the behavior of an expert by using a dataset composed of only state-action pairs demonstrated by the expert, without any additional interaction with the environment. However, During deployment, the policy observations may contain measurement errors or adversarial disturbances. Since the observations may deviate from the true states, they can mislead the agent into making sub-optimal actions. In this work, we use a global Lipschitz regularization approach to enhance the robustness of the learned policy network. We then show that the resulting global Lipschitz property provides a robustness certificate to the policy with respect to different bounded norm perturbations. Then, we propose a way to construct a Lipschitz neural network that ensures the policy robustness. We empirically validate our theory across various environments in Gymnasium. Keywords: Robust Reinforcement Learning; Behavior Cloning; Lipschitz Neural Network