mlsanityData to 14 Oct 2026

On the Sample Complexity of Stability Constrained Imitation Learning

arXiv 2102.09161 ↗First posted 18 Feb 2021cs.LG cs.SY eess.SYcited by 38

On the map: Offline RL and imitation learning from data → Imitation learning methods

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.

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.

Builds on

20 of 42 references.

Closest ancestors · 5

Same direction, newest first

  1. 2020Imitation Learning with Stability and Safety Guarantees16 Dec
  2. 2018An Algorithmic Perspective on Imitation Learning16 Nov
  3. 2018EnsembleDAgger: A Bayesian Approach to Safe Imitation Learning22 Jul
  4. 2018Learning Contracting Vector Fields For Stable Imitation Learning13 Apr
  5. 2018Safe end-to-end imitation learning for model predictive control27 Mar

Other references · 15

  1. 2015Trust Region Policy Optimizationcited by 2,580
  2. 2017End-to-end Driving via Conditional Imitation Learningcited by 485
  3. 2017DART: Noise Injection for Robust Imitation Learningcited by 191
  4. 2020Neural Lyapunov Controlcited by 142
  5. 2018Algorithmic Framework for Model-based Deep Reinforcement Learning with Theoretical Guaranteescited by 140
  6. 2020Learning Stable Deep Dynamics Modelscited by 111
  7. 2017Deeply AggreVaTeD: Differentiable Imitation Learning for Sequential Predictioncited by 93
  8. 2018Learning an Approximate Model Predictive Controller with Guaranteescited by 57
  9. 2020Probably Approximately Correct Constrained Learningcited by 47
  10. 2020Learning Stability Certificates from Datacited by 45
  11. 2019Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularizationcited by 32
  12. 2020Regret Bounds for Adaptive Nonlinear Controlcited by 25
3 more
  1. 2018Beyond Convexity -- Contraction and Global Convergence of Gradient Descentcited by 17
  2. 2017DropoutDAgger: A Bayesian Approach to Safe Imitation Learningcited by 14
  3. 2018Data Driven Stability Analysis of Black-box Switched Linear Systemscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 6; 2022: 11; 2023: 9; 2024: 5; 2025: 4; 2026: 3.

38 papers.

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  1. 2023Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardwarecited by 1,568
  2. 2021Implicit Behavioral Cloningcited by 452
  3. 2021Imitation Learning: Progress, Taxonomies and Challengescited by 58
  4. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 53
  5. 2023Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behaviorcited by 33
  6. 2022Lyapunov Density Models: Constraining Distribution Shift in Learning-Based Controlcited by 28
  7. 2022Single Trajectory Nonparametric Learning of Nonlinear Dynamicscited by 26
  8. 2022Reproducibility in Optimization: Theoretical Framework and Limitscited by 21
  9. 2022TaSIL: Taylor Series Imitation Learningcited by 21
  10. 2023One ACT Play: Single Demonstration Behavior Cloning with Action Chunking Transformerscited by 17
  11. 2023Butterfly Effects of SGD Noise: Error Amplification in Behavior Cloning and Autoregressioncited by 14
  12. 2023CCIL: Context-conditioned imitation learning for urban drivingcited by 12
26 more
  1. 2022How are policy gradient methods affected by the limits of control?cited by 10
  2. 2023Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictionscited by 8
  3. 2021Communication Topology Co-Design in Graph Recurrent Neural Network Based Distributed Controlcited by 7
  4. 2022Risk Verification of Stochastic Systems with Neural Network Controllerscited by 6
  5. 2022Towards a Theoretical Foundation of Policy Optimization for Learning Control Policiescited by 6
  6. 2022Model Predictive Control via On-Policy Imitation Learningcited by 6
  7. 2024IDIL: Imitation Learning of Intent-Driven Expert Behaviorcited by 5
  8. 2025Real-Time Operator Takeover for Visuomotor Diffusion Policy Trainingcited by 5
  9. 2023Unlabeled Imperfect Demonstrations in Adversarial Imitation Learningcited by 3
  10. 2023On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Controlcited by 3
  11. 2026ELITE: Experiential Learning and Intent-Aware Transfer for Self-improving Embodied Agentscited by 3
  12. 2021Adversarially Robust Stability Certificates can be Sample-Efficientcited by 2
  13. 2022Fail-Safe Adversarial Generative Imitation Learningcited by 2
  14. 2025Language Model Distillation: A Temporal Difference Imitation Learning Perspectivecited by 2
  15. 2025FABG : End-to-end Imitation Learning for Embodied Affective Human-Robot Interactioncited by 1
  16. 2025Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomycited by 1
  17. 2021Learning Lipschitz Feedback Policies from Expert Demonstrations: Closed-Loop Guarantees, Generalization and Robustnesscited by 0
  18. 2021Discrete fully probabilistic design: towards a control pipeline for the synthesis of policies from examplescited by 0
  19. 2022Cross apprenticeship learning framework: Properties and solution approachescited by 0
  20. 2023Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Setscited by 0
  21. 2024Visual Imitation Learning with Calibrated Contrastive Representationcited by 0
  22. 2024Towards Improving Learning from Demonstration Algorithms via MCMC Methodscited by 0
  23. 2024Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Controlcited by 0
  24. 2024Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problemcited by 0
  25. 2026Primary-Fine Decoupling for Action Generation in Robotic Imitationcited by 0
  26. 2026FocalPolicy: Frequency-Optimized Chunking and Locally Anchored Flow Matching for Coherent Visuomotor Policycited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025The Pitfalls of Imitation Learning when Actions are Continuous
  2. 2021Provably Breaking the Quadratic Error Compounding Barrier in Imitation Learning, Optimally
  3. 2024Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning
  4. 2020Toward the Fundamental Limits of Imitation Learning
  5. 2025Action Chunking and Exploratory Data Collection Yield Exponential Improvements in Behavior Cloning for Continuous Control
  6. 2024Stable-BC: Controlling Covariate Shift with Stable Behavior Cloning
  7. 2024Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recovery
  8. 2026Learning When to Stop: Selective Imitation Learning Under Arbitrary Dynamics Shift