mlsanityData to 7 Oct 2026

Learning Contracting Vector Fields For Stable Imitation Learning

arXiv 1804.04878 ↗First posted 13 Apr 2018cs.RO cs.LG stat.MLcited by 20

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

Abstract (arXiv)

We propose a new non-parametric framework for learning incrementally stable dynamical systems x' = f(x) from a set of sampled trajectories. We construct a rich family of smooth vector fields induced by certain classes of matrix-valued kernels, whose equilibria are placed exactly at a desired set of locations and whose local contraction and curvature properties at various points can be explicitly controlled using convex optimization. With curl-free kernels, our framework may also be viewed as a mechanism to learn potential fields and gradient flows. We develop large-scale techniques using randomized kernel approximations in this context. We demonstrate our approach, called contracting vector fields (CVF), on imitation learning tasks involving complex point-to-point human handwriting motions.

Key facts. Cited by 20 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 3 of its 30 references that are in the map. First posted on arXiv 13 Apr 2018.

Builds on

3 of 30 references.

References · 3

  1. 2016Random Fourier Features for Operator-Valued Kernelscited by 22
  2. 2016Operator-Valued Bochner Theorem, Fourier Feature Maps for Operator-Valued Kernels, and Vector-Valued Learningcited by 15
  3. 2014Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causalitycited by 13

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Cited by year

Citing papers per year: 2021: 3; 2022: 3; 2023: 5; 2024: 8; 2025: 1.

20 papers.

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  1. 2021On the Sample Complexity of Stability Constrained Imitation Learningcited by 38
  2. 2022TaSIL: Taylor Series Imitation Learningcited by 21
  3. 2024Neural Contractive Dynamical Systemscited by 14
  4. 2024Learning Neural Contracting Dynamics: Extended Linearization and Global Guaranteescited by 11
  5. 2021Nonparametric adaptive control and prediction: theory and randomized algorithmscited by 8
  6. 2025Predictability Enables Parallelization of Nonlinear State Space Modelscited by 7
  7. 2023Data-Driven Control with Inherent Lyapunov Stabilitycited by 6
  8. 2023Learning Control-Oriented Dynamical Structure from Datacited by 5
  9. 2023MMP++: Motion Manifold Primitives with Parametric Curve Modelscited by 5
  10. 2024Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recoverycited by 5
  11. 2022Multiscale Sensor Fusion and Continuous Control with Neural CDEscited by 4
  12. 2024Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overviewcited by 3
8 more
  1. 2021Adversarially Robust Stability Certificates can be Sample-Efficientcited by 2
  2. 2023Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spacescited by 2
  3. 2024Learning Dynamical Systems Encoding Non-Linearity within Space Curvaturecited by 2
  4. 2022Linearization and Identification of Multiple-Attractor Dynamical Systems through Laplacian Eigenmapscited by 1
  5. 2023Learning Orbitally Stable Systems for Diagrammatically Teachingcited by 1
  6. 2024Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regionscited by 1
  7. 2024Learning to Represent Surroundings, Anticipate Motion and Take Informed Actions in Unstructured Environmentscited by 0
  8. 2024Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier featurescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Learning Lyapunov-Stable Polynomial Dynamical Systems through Imitation
  2. 2025Scalable Learning of High-Dimensional Demonstrations with Composition of Linear Parameter Varying Dynamical Systems
  3. 2023PUMA: Deep Metric Imitation Learning for Stable Motion Primitives
  4. 2022Multi-Task Imitation Learning for Linear Dynamical Systems
  5. 2026SPREAD: Subspace Representation Distillation for Lifelong Imitation Learning
  6. 2023Stable Motion Primitives via Imitation and Contrastive Learning ↗
  7. 2024Learning from Demonstration with Implicit Nonlinear Dynamics Models
  8. 2019A Linearly Constrained Nonparametric Framework for Imitation Learning