# Stable-BC: Controlling Covariate Shift with Stable Behavior Cloning

arXiv: https://arxiv.org/abs/2408.06246 · HTML: https://mlsanity.com/paper/2408.06246/

## Key facts

- Cited by 15 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.
- First posted on arXiv 12 Aug 2024.

## Placed in

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

## Built on by (most cited first, 15 of 15)

- [Good SFT Optimizes for SFT, Better SFT Prepares for Reinforcement Learning](https://mlsanity.com/paper/2602.01058/) (2026)
- [Elastic Motion Policy: An Adaptive Dynamical System for Robust and Efficient One-Shot Imitation Learning](https://mlsanity.com/paper/2503.08029/) (2025)
- [Lagrangian Perturbation Diffusion Steering: Latent Reinforcement Learning for Generative Policies](https://mlsanity.com/paper/2606.01151/) (2026)
- [λ: A Benchmark for Data-Efficiency in Long-Horizon Indoor Mobile Manipulation Robotics](https://mlsanity.com/paper/2412.05313/) (2024)
- [Counterfactual Behavior Cloning: Offline Imitation Learning from Imperfect Human Demonstrations](https://mlsanity.com/paper/2505.10760/) (2025)
- [Safety-Aware Imitation Learning via MPC-Guided Disturbance Injection](https://mlsanity.com/paper/2508.03129/) (2025)
- [Continuous Vision-Language-Action Co-Learning with Semantic-Physical Alignment for Behavioral Cloning](https://mlsanity.com/paper/2511.14396/) (2025)
- [Curiosity-Diffuser: Curiosity Guide Diffusion Models for Reliability](https://mlsanity.com/paper/2503.14833/) (2025)
- [Denoising-based Contractive Imitation Learning](https://mlsanity.com/paper/2503.15918/) (2025)
- [Learning Robust Visuomotor Policies via Dynamics Alignment](https://mlsanity.com/paper/2510.27114/) (2025)
- [How to Mitigate the Distribution Shift Problem in Robotics Control: A Robust and Adaptive Approach Based on Offline to Online Imitation Learning](https://mlsanity.com/paper/2605.25414/) (2026)
- [ReGuide: From Test-Time Guidance to Self-Improving Diffusion Policies](https://mlsanity.com/paper/2606.28939/) (2026)
- [IL-ACT: Imitation Learning with Adaptive Cartesian Tracking Control for a 30-ton Excavator](https://mlsanity.com/paper/2609.16696/) (2026)
- [DriftOPD: Sequence-Level Reverse-KL Distillation for One-Step VLA Policies](https://mlsanity.com/paper/2610.00317/) (2026)
- [Where Small Mistakes Matter: Quantifying State Criticality for Imitation Learning](https://mlsanity.com/paper/2610.17709/) (2026)

## Abstract (arXiv)

Behavior cloning is a common imitation learning paradigm. Under behavior cloning the robot collects expert demonstrations, and then trains a policy to match the actions taken by the expert. This works well when the robot learner visits states where the expert has already demonstrated the correct action; but inevitably the robot will also encounter new states outside of its training dataset. If the robot learner takes the wrong action at these new states it could move farther from the training data, which in turn leads to increasingly incorrect actions and compounding errors. Existing works try to address this fundamental challenge by augmenting or enhancing the training data. By contrast, in our paper we develop the control theoretic properties of behavior cloned policies. Specifically, we consider the error dynamics between the system's current state and the states in the expert dataset. From the error dynamics we derive model-based and model-free conditions for stability: under these conditions the robot shapes its policy so that its current behavior converges towards example behaviors in the expert dataset. In practice, this results in Stable-BC, an easy to implement extension of standard behavior cloning that is provably robust to covariate shift. We demonstrate the effectiveness of our algorithm in simulations with interactive, nonlinear, and visual environments. We also conduct experiments where a robot arm uses Stable-BC to play air hockey. See our website here: https://collab.me.vt.edu/Stable-BC/