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KEEC: Koopman Embedded Equivariant Control

arXiv 2312.01544 ↗First posted 4 Dec 2023cs.LG cs.AI cs.SYcited by 0

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Abstract (arXiv)

An efficient way to control systems with unknown nonlinear dynamics is to find an appropriate embedding or representation for simplified approximation (e.g. linearization), which facilitates system identification and control synthesis. Nevertheless, there has been a lack of embedding methods that can guarantee (i) embedding the dynamical system comprehensively, including the vector fields (ODE form) of the dynamics, and (ii) preserving the consistency of control effect between the original and latent space. To address these challenges, we propose Koopman Embedded Equivariant Control (KEEC) to learn an embedding of the states and vector fields such that a Koopman operator is approximated as the latent dynamics. Due to the Koopman operator's linearity, learning the latent vector fields of the dynamics becomes simply solving linear equations. Thus in KEEC, the analytical form of the greedy control policy, which is dependent on the learned differential information of the dynamics and value function, is also simplified. Meanwhile, KEEC preserves the effectiveness of the control policy in the latent space by preserving the metric in two spaces. Our algorithm achieves superior performances in the experiments conducted on various control domains, including the image-based Pendulum, Lorenz-63 and the wave equation. The code is available at https://github.com/yyimingucl/Koopman-Embedded-Equivariant-Control.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 38 of its 80 references that are in the map. First posted on arXiv 4 Dec 2023.

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References · 38

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2023GPT-4 Technical Reportcited by 18,132
  3. 2022Training language models to follow instructions with human feedbackcited by 15,712
  4. 2017Proximal Policy Optimization Algorithmscited by 14,441
  5. 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 12,865
  6. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,635
  7. 2015Continuous control with deep reinforcement learningcited by 3,279
  8. 2015High-Dimensional Continuous Control Using Generalized Advantage Estimationcited by 1,916
  9. 2020Conservative Q-Learning for Offline Reinforcement Learningcited by 1,777
  10. 2021Decision Transformer: Reinforcement Learning via Sequence Modelingcited by 1,528
  11. 2018World Modelscited by 1,444
  12. 2021Offline Reinforcement Learning with Implicit Q-Learningcited by 1,245
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  1. 2016Geometric deep learning: going beyond Euclidean datacited by 1,042
  2. 2021A Minimalist Approach to Offline Reinforcement Learningcited by 882
  3. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 748
  4. 2019Model-Based Reinforcement Learning for Ataricited by 495
  5. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  6. 2017Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuningcited by 288
  7. 2021Modern Koopman Theory for Dynamical Systemscited by 269
  8. 2015Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Imagescited by 266
  9. 2018Visual Reinforcement Learning with Imagined Goalscited by 248
  10. 2022SO(2)-Equivariant Reinforcement Learningcited by 79
  11. 2019Learning Compositional Koopman Operators for Model-Based Controlcited by 67
  12. 2019Variational Inference MPC for Bayesian Model-based Reinforcement Learningcited by 39
  13. 2017Robust Locally-Linear Controllable Embeddingcited by 37
  14. 2021Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamicscited by 27
  15. 2019Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Controlcited by 22
  16. 2016Linear identification of nonlinear systems: A lifting technique based on the Koopman operatorcited by 18
  17. 2021Average-Reward Reinforcement Learning with Trust Region Methodscited by 18
  18. 2019Prediction, Consistency, Curvature: Representation Learning for Locally-Linear Controlcited by 17
  19. 2022Unsupervised Learning of Equivariant Structure from Sequencescited by 15
  20. 2023Neural Fourier Transform: A General Approach to Equivariant Representation Learningcited by 12
  21. 2018Nonlinear System Identification of Soft Robot Dynamics Using Koopman Operator Theorycited by 7
  22. 2020Neural Lyapunov Model Predictive Control: Learning Safe Global Controllers from Sub-optimal Examplescited by 5
  23. 2023Representing and Learning Functions Invariant Under Crystallographic Groupscited by 5
  24. 2022On a Mechanism Framework of Autoencoderscited by 3
  25. 2018On projective and affine equivalence of sub-Riemannian metricscited by 1
  26. 2020Further Geometric and Lyapunov Characterizations of Incrementally Stable Systems on Finsler Manifoldscited by 1

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