mlsanityData to 7 Oct 2026

Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recovery

arXiv 2412.07544 ↗First posted 10 Dec 2024cs.LG cs.RO stat.MLcited by 5

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

Abstract (arXiv)

Imitation learning is a data-driven approach to learning policies from expert behavior, but it is prone to unreliable outcomes in out-of-sample (OOS) regions. While previous research relying on stable dynamical systems guarantees convergence to a desired state, it often overlooks transient behavior. We propose a framework for learning policies modeled by contractive dynamical systems, ensuring that all policy rollouts converge regardless of perturbations, and in turn, enable efficient OOS recovery. By leveraging recurrent equilibrium networks and coupling layers, the policy structure guarantees contractivity for any parameter choice, which facilitates unconstrained optimization. We also provide theoretical upper bounds for worst-case and expected loss to rigorously establish the reliability of our method in deployment. Empirically, we demonstrate substantial OOS performance improvements for simulated robotic manipulation and navigation tasks.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data. Builds on 32 of its 51 references that are in the map. First posted on arXiv 10 Dec 2024.

Builds on

32 of 51 references.

Closest ancestors · 6

Same direction, newest first

  1. 2024Globally Stable Neural Imitation Policies7 Mar
  2. 2023Learning Lyapunov-Stable Polynomial Dynamical Systems through Imitation31 Oct
  3. 2018Variational Discriminator Bottleneck: Improving Imitation Learning, Inverse RL, and GANs by Constraining Information Flow1 Oct
  4. 2018EnsembleDAgger: A Bayesian Approach to Safe Imitation Learning22 Jul
  5. 2018Behavioral Cloning from Observation4 May
  6. 2018Learning Contracting Vector Fields For Stable Imitation Learning13 Apr

Other references · 26

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2023Diffusion Policy: Visuomotor Policy Learning via Action Diffusioncited by 2,730
  4. 2016Density estimation using Real NVPcited by 2,029
  5. 2016Generative Adversarial Imitation Learningcited by 1,576
  6. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  7. 2021What Matters in Learning from Offline Human Demonstrations for Robot Manipulationcited by 699
  8. 2017Learning Robust Rewards with Adversarial Inverse Reinforcement Learningcited by 485
  9. 2017Soft-DTW: a Differentiable Loss Function for Time-Seriescited by 265
  10. 2023Orbit: A Unified Simulation Framework for Interactive Robot Learning Environmentscited by 239
  11. 2017DART: Noise Injection for Robust Imitation Learningcited by 187
  12. 2022Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methodscited by 148
14 more
  1. 2020Learning to Generalize Across Long-Horizon Tasks from Human Demonstrationscited by 114
  2. 2020Learning Stable Deep Dynamics Modelscited by 110
  3. 2020Neural Dynamic Policies for End-to-End Sensorimotor Learningcited by 56
  4. 2021Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustnesscited by 43
  5. 2021Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overviewcited by 42
  6. 2015Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Designcited by 38
  7. 2020Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systemscited by 32
  8. 2022Learning Riemannian Stable Dynamical Systems via Diffeomorphismscited by 17
  9. 2024Neural Contractive Dynamical Systemscited by 14
  10. 2023Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equationscited by 8
  11. 2024Learning Deep Dynamical Systems using Stable Neural ODEscited by 8
  12. 2024Learning to optimize with convergence guarantees using nonlinear system theorycited by 7
  13. 2024A PAC-Bayesian Framework for Optimal Control with Stability Guaranteescited by 7
  14. 2021A unified framework for walking and running of bipedal robotscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 2.

5 papers.

  1. 2025R2DN: Scalable Parameterization of Contracting and Lipschitz Recurrent Deep Networkscited by 2
  2. 2025Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representationscited by 1
  3. 2026Contractive Diffusion Policies: Robust Action Diffusion via Contractive Score-Based Sampling with Differential Equationscited by 1
  4. 2025Denoising-based Contractive Imitation Learningcited by 0
  5. 2026IL-ACT: Imitation Learning with Adaptive Cartesian Tracking Control for a 30-ton Excavatorcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Elastic Motion Policy: An Adaptive Dynamical System for Robust and Efficient One-Shot Imitation Learning
  2. 2025CCDP: Composition of Conditional Diffusion Policies with Guided Sampling
  3. 2023End-to-End Stable Imitation Learning via Autonomous Neural Dynamic Policies
  4. 2025The Pitfalls of Imitation Learning when Actions are Continuous
  5. 2025Theoretical Closed-loop Stability Bounds for Dynamical System Coupled with Diffusion Policies
  6. 2021On the Sample Complexity of Stability Constrained Imitation Learning
  7. 2018Dynamic Regret Convergence Analysis and an Adaptive Regularization Algorithm for On-Policy Robot Imitation Learning
  8. 2024Stable-BC: Controlling Covariate Shift with Stable Behavior Cloning