mlsanityData to 14 Oct 2026

Equivariant Q Learning in Spatial Action Spaces

arXiv 2110.15443 ↗First posted 28 Oct 2021cs.ROcited by 62

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Abstract (arXiv)

Recently, a variety of new equivariant neural network model architectures have been proposed that generalize better over rotational and reflectional symmetries than standard models. These models are relevant to robotics because many robotics problems can be expressed in a rotationally symmetric way. This paper focuses on equivariance over a visual state space and a spatial action space -- the setting where the robot action space includes a subset of rmSE(2). In this situation, we know a priori that rotations and translations in the state image should result in the same rotations and translations in the spatial action dimensions of the optimal policy. Therefore, we can use equivariant model architectures to make Q learning more sample efficient. This paper identifies when the optimal Q function is equivariant and proposes Q network architectures for this setting. We show experimentally that this approach outperforms standard methods in a set of challenging manipulation problems.

Key facts. Cited by 62 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 Oct 2021.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 11; 2023: 12; 2024: 12; 2025: 16; 2026: 11.

62 papers.

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  1. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 97
  2. 2024Equivariant Diffusion Policycited by 66
  3. 2024Theia: Distilling Diverse Vision Foundation Models for Robot Learningcited by 61
  4. 2023Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulationcited by 52
  5. 2024Does equivariance matter at scale?cited by 52
  6. 2023Geometric Algebra Transformercited by 48
  7. 2022Equivariant Transporter Networkcited by 46
  8. 2022Edge Grasp Network: A Graph-Based SE(3)-invariant Approach to Grasp Detectioncited by 35
  9. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 33
  10. 2024Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3Dcited by 33
  11. 2023Equivariant plug-and-play image reconstructioncited by 26
  12. 2022SEIL: Simulation-augmented Equivariant Imitation Learningcited by 23
38 more
  1. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 23
  2. 2022Equi-Tuning: Group Equivariant Fine-Tuning of Pretrained Modelscited by 22
  3. 2022Maximum Class Separation as Inductive Bias in One Matrixcited by 21
  4. 2023A General Theory of Correct, Incorrect, and Extrinsic Equivariancecited by 19
  5. 2023Leveraging Symmetries in Pick and Placecited by 19
  6. 2024Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policiescited by 18
  7. 2024Equivariant Reinforcement Learning under Partial Observabilitycited by 18
  8. 2022Relational Reasoning via Set Transformers: Provable Efficiency and Applications to MARLcited by 12
  9. 2023On Robot Grasp Learning Using Equivariant Modelscited by 12
  10. 2023Efficient Equivariant Transfer Learning from Pretrained Modelscited by 11
  11. 2022Continual Vision-based Reinforcement Learning with Group Symmetriescited by 10
  12. 2024Learning from 10 Demos: Generalisable and Sample-Efficient Policy Learning with Oriented Affordance Framescited by 10
  13. 2025SE(3)-Equivariant Robot Learning and Control: A Tutorial Surveycited by 10
  14. 2025SE(3)-Equivariant Diffusion Policy in Spherical Fourier Spacecited by 8
  15. 2022Learning Fabric Manipulation in the Real World with Human Videoscited by 7
  16. 2023SO(2)-Equivariant Downwash Models for Close Proximity Flightcited by 7
  17. 2023Understanding when Dynamics-Invariant Data Augmentations Benefit Model-Free Reinforcement Learning Updatescited by 7
  18. 2024Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networkscited by 7
  19. 2024MATCH POLICY: A Simple Pipeline from Point Cloud Registration to Manipulation Policiescited by 6
  20. 2025Constraint-Preserving Data Generation for Visuomotor Policy Learningcited by 6
  21. 2025Explicit Discovery of Nonlinear Symmetries from Dynamic Datacited by 6
  22. 2023QDP: Learning to Sequentially Optimise Quasi-Static and Dynamic Manipulation Primitives for Robotic Cloth Manipulationcited by 5
  23. 2025A Practical Guide for Incorporating Symmetry in Diffusion Policycited by 5
  24. 20253D Equivariant Visuomotor Policy Learning via Spherical Projectioncited by 5
  25. 2024Equivariant Ensembles and Regularization for Reinforcement Learning in Map-based Path Planningcited by 4
  26. 2025EfficientFlow: Efficient Equivariant Flow Policy Learning for Embodied AIcited by 4
  27. 2023Learning from Pixels with Expert Observationscited by 3
  28. 2025Partially Equivariant Reinforcement Learning in Symmetry-Breaking Environmentscited by 3
  29. 2024Leveraging Symmetry to Accelerate Learning of Trajectory Tracking Controllers for Free-Flying Robotic Systemscited by 2
  30. 2025Coarse-to-Fine 3D Keyframe Transportercited by 2
  31. 2026Approximate Equivariance via Projection-based Regularisationcited by 2
  32. 2025Symmetries-enhanced Multi-Agent Reinforcement Learningcited by 1
  33. 2025Learning Abstract World Models with a Group-Structured Latent Spacecited by 1
  34. 2025Equivariant Volumetric Graspingcited by 1
  35. 2025On Uncertainty Calibration for Equivariant Functionscited by 1
  36. 2026PRISM: Parallel Reward Integration with Symmetry for MORLcited by 1
  37. 2026Learning Equivariant Neural-Augmented Object Dynamics From Few Interactionscited by 1
  38. 2026Groupoid-Based Internal State Representations for Reinforcement Learning with Local Symmetriescited by 1

50 most cited of 62 All 62 (JSON)