# Globally Stable Neural Imitation Policies

arXiv: https://arxiv.org/abs/2403.04118 · HTML: https://mlsanity.com/paper/2403.04118/

## Key facts

- Cited by 3 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 12 of its 28 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Placed in

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

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Behavioral Cloning from Observation](https://mlsanity.com/paper/1805.01954/) (2018)
- [Learning Robust Rewards with Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1710.11248/) (2017)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [Lyapunov-stable neural-network control](https://mlsanity.com/paper/2109.14152/) (2021)
- [Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems](https://mlsanity.com/paper/2005.13143/) (2020)
- [Learning Riemannian Stable Dynamical Systems via Diffeomorphisms](https://mlsanity.com/paper/2211.03169/) (2022)
- [Learning Lyapunov-Stable Polynomial Dynamical Systems through Imitation](https://mlsanity.com/paper/2310.20605/) (2023)
- [Generating Stable and Collision-Free Policies through Lyapunov Function Learning](https://mlsanity.com/paper/2211.08976/) (2022)

## Built on by (most cited first, 3 of 3)

- [Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recovery](https://mlsanity.com/paper/2412.07544/) (2024)
- [Single-Shot Learning of Stable Dynamical Systems for Long-Horizon Manipulation Tasks](https://mlsanity.com/paper/2410.01033/) (2024)
- [Contractive Diffusion Policies: Robust Action Diffusion via Contractive Score-Based Sampling with Differential Equations](https://mlsanity.com/paper/2601.01003/) (2026)

## Abstract (arXiv)

Imitation learning presents an effective approach to alleviate the resource-intensive and time-consuming nature of policy learning from scratch in the solution space. Even though the resulting policy can mimic expert demonstrations reliably, it often lacks predictability in unexplored regions of the state-space, giving rise to significant safety concerns in the face of perturbations. To address these challenges, we introduce the Stable Neural Dynamical System (SNDS), an imitation learning regime which produces a policy with formal stability guarantees. We deploy a neural policy architecture that facilitates the representation of stability based on Lyapunov theorem, and jointly train the policy and its corresponding Lyapunov candidate to ensure global stability. We validate our approach by conducting extensive experiments in simulation and successfully deploying the trained policies on a real-world manipulator arm. The experimental results demonstrate that our method overcomes the instability, accuracy, and computational intensity problems associated with previous imitation learning methods, making our method a promising solution for stable policy learning in complex planning scenarios.