# On the Sample Complexity of Stability Constrained Imitation Learning

arXiv: https://arxiv.org/abs/2102.09161 · HTML: https://mlsanity.com/paper/2102.09161/

## Key facts

- Cited by 38 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 20 of its 42 references that are in the map.
- First posted on arXiv 18 Feb 2021.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [DART: Noise Injection for Robust Imitation Learning](https://mlsanity.com/paper/1703.09327/) (2017)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Algorithmic Framework for Model-based Deep Reinforcement Learning with Theoretical Guarantees](https://mlsanity.com/paper/1807.03858/) (2018)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [EnsembleDAgger: A Bayesian Approach to Safe Imitation Learning](https://mlsanity.com/paper/1807.08364/) (2018)
- [Deeply AggreVaTeD: Differentiable Imitation Learning for Sequential Prediction](https://mlsanity.com/paper/1703.01030/) (2017)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [Probably Approximately Correct Constrained Learning](https://mlsanity.com/paper/2006.05487/) (2020)
- [Learning Stability Certificates from Data](https://mlsanity.com/paper/2008.05952/) (2020)
- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization](https://mlsanity.com/paper/1907.13122/) (2019)
- [Regret Bounds for Adaptive Nonlinear Control](https://mlsanity.com/paper/2011.13101/) (2020)
- [Learning Contracting Vector Fields For Stable Imitation Learning](https://mlsanity.com/paper/1804.04878/) (2018)
- [Beyond Convexity -- Contraction and Global Convergence of Gradient Descent](https://mlsanity.com/paper/1806.06655/) (2018)
- [DropoutDAgger: A Bayesian Approach to Safe Imitation Learning](https://mlsanity.com/paper/1709.06166/) (2017)
- [Safe end-to-end imitation learning for model predictive control](https://mlsanity.com/paper/1803.10231/) (2018)
- [Data Driven Stability Analysis of Black-box Switched Linear Systems](https://mlsanity.com/paper/1803.03687/) (2018)

## Built on by (most cited first, 30 of 38)

- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Imitation Learning: Progress, Taxonomies and Challenges](https://mlsanity.com/paper/2106.12177/) (2021)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior](https://mlsanity.com/paper/2307.14619/) (2023)
- [Lyapunov Density Models: Constraining Distribution Shift in Learning-Based Control](https://mlsanity.com/paper/2206.10524/) (2022)
- [Single Trajectory Nonparametric Learning of Nonlinear Dynamics](https://mlsanity.com/paper/2202.08311/) (2022)
- [Reproducibility in Optimization: Theoretical Framework and Limits](https://mlsanity.com/paper/2202.04598/) (2022)
- [TaSIL: Taylor Series Imitation Learning](https://mlsanity.com/paper/2205.14812/) (2022)
- [One ACT Play: Single Demonstration Behavior Cloning with Action Chunking Transformers](https://mlsanity.com/paper/2309.10175/) (2023)
- [Butterfly Effects of SGD Noise: Error Amplification in Behavior Cloning and Autoregression](https://mlsanity.com/paper/2310.11428/) (2023)
- [CCIL: Context-conditioned imitation learning for urban driving](https://mlsanity.com/paper/2305.02649/) (2023)
- [How are policy gradient methods affected by the limits of control?](https://mlsanity.com/paper/2206.06863/) (2022)
- [Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictions](https://mlsanity.com/paper/2307.10524/) (2023)
- [Communication Topology Co-Design in Graph Recurrent Neural Network Based Distributed Control](https://mlsanity.com/paper/2104.13868/) (2021)
- [Risk Verification of Stochastic Systems with Neural Network Controllers](https://mlsanity.com/paper/2209.09881/) (2022)
- [Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies](https://mlsanity.com/paper/2210.04810/) (2022)
- [Model Predictive Control via On-Policy Imitation Learning](https://mlsanity.com/paper/2210.09206/) (2022)
- [IDIL: Imitation Learning of Intent-Driven Expert Behavior](https://mlsanity.com/paper/2404.16989/) (2024)
- [Real-Time Operator Takeover for Visuomotor Diffusion Policy Training](https://mlsanity.com/paper/2502.02308/) (2025)
- [Unlabeled Imperfect Demonstrations in Adversarial Imitation Learning](https://mlsanity.com/paper/2302.06271/) (2023)
- [On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control](https://mlsanity.com/paper/2306.01914/) (2023)
- [ELITE: Experiential Learning and Intent-Aware Transfer for Self-improving Embodied Agents](https://mlsanity.com/paper/2603.24018/) (2026)
- [Adversarially Robust Stability Certificates can be Sample-Efficient](https://mlsanity.com/paper/2112.10690/) (2021)
- [Fail-Safe Adversarial Generative Imitation Learning](https://mlsanity.com/paper/2203.01696/) (2022)
- [Language Model Distillation: A Temporal Difference Imitation Learning Perspective](https://mlsanity.com/paper/2505.20335/) (2025)
- [FABG : End-to-end Imitation Learning for Embodied Affective Human-Robot Interaction](https://mlsanity.com/paper/2503.01363/) (2025)
- [Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomy](https://mlsanity.com/paper/2512.17899/) (2025)
- [Learning Lipschitz Feedback Policies from Expert Demonstrations: Closed-Loop Guarantees, Generalization and Robustness](https://mlsanity.com/paper/2103.16629/) (2021)
- [Discrete fully probabilistic design: towards a control pipeline for the synthesis of policies from examples](https://mlsanity.com/paper/2112.11210/) (2021)

## Abstract (arXiv)

We study the following question in the context of imitation learning for continuous control: how are the underlying stability properties of an expert policy reflected in the sample-complexity of an imitation learning task? We provide the first results showing that a surprisingly granular connection can be made between the underlying expert system's incremental gain stability, a novel measure of robust convergence between pairs of system trajectories, and the dependency on the task horizon T of the resulting generalization bounds. In particular, we propose and analyze incremental gain stability constrained versions of behavior cloning and a DAgger-like algorithm, and show that the resulting sample-complexity bounds naturally reflect the underlying stability properties of the expert system. As a special case, we delineate a class of systems for which the number of trajectories needed to achieve varepsilon-suboptimality is sublinear in the task horizon T, and do so without requiring (strong) convexity of the loss function in the policy parameters. Finally, we conduct numerical experiments demonstrating the validity of our insights on both a simple nonlinear system for which the underlying stability properties can be easily tuned, and on a high-dimensional quadrupedal robotic simulation.