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SO(2)-Equivariant Reinforcement Learning

arXiv 2203.04439 ↗First posted 8 Mar 2022cs.ROcited by 79

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Abstract (arXiv)

Equivariant neural networks enforce symmetry within the structure of their convolutional layers, resulting in a substantial improvement in sample efficiency when learning an equivariant or invariant function. Such models are applicable to robotic manipulation learning which can often be formulated as a rotationally symmetric problem. This paper studies equivariant model architectures in the context of Q-learning and actor-critic reinforcement learning. We identify equivariant and invariant characteristics of the optimal Q-function and the optimal policy and propose equivariant DQN and SAC algorithms that leverage this structure. We present experiments that demonstrate that our equivariant versions of DQN and SAC can be significantly more sample efficient than competing algorithms on an important class of robotic manipulation problems.

Key facts. Cited by 79 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Mar 2022.

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Citing papers per year: 2022: 10; 2023: 18; 2024: 18; 2025: 22; 2026: 11.

79 papers.

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  1. 2024EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learningcited by 72
  2. 2024Equivariant Diffusion Policycited by 61
  3. 2022Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learningcited by 54
  4. 2023Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulationcited by 51
  5. 2024Does equivariance matter at scale?cited by 49
  6. 2023EDGI: Equivariant Diffusion for Planning with Embodied Agentscited by 35
  7. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 32
  8. 2024Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3Dcited by 32
  9. 2022Continuous MDP Homomorphisms and Homomorphic Policy Gradientcited by 24
  10. 2022SEIL: Simulation-augmented Equivariant Imitation Learningcited by 22
  11. 2023Learning to Extrapolate: A Transductive Approachcited by 19
  12. 2023A General Theory of Correct, Incorrect, and Extrinsic Equivariancecited by 18
38 more
  1. 2024Symmetry Considerations for Learning Task Symmetric Robot Policiescited by 18
  2. 2024Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policiescited by 18
  3. 2024Equivariant Reinforcement Learning under Partial Observabilitycited by 17
  4. 2022Equivariant Networks for Zero-Shot Coordinationcited by 16
  5. 2023One-shot Imitation Learning via Interaction Warpingcited by 16
  6. 2022Unsupervised Learning of Equivariant Structure from Sequencescited by 15
  7. 2022Relational Reasoning via Set Transformers: Provable Efficiency and Applications to MARLcited by 12
  8. 2023On Robot Grasp Learning Using Equivariant Modelscited by 12
  9. 2024RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentationcited by 12
  10. 2022Continual Vision-based Reinforcement Learning with Group Symmetriescited by 10
  11. 2025Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objectscited by 10
  12. 2023Sample Efficient Reinforcement Learning in Mixed Systems through Augmented Samples and Its Applications to Queueing Networkscited by 9
  13. 2023ESP: Exploiting Symmetry Prior for Multi-Agent Reinforcement Learningcited by 9
  14. 2024Approximate Equivariance in Reinforcement Learningcited by 9
  15. 2023Policy Gradient Methods in the Presence of Symmetries and State Abstractionscited by 8
  16. 2025SE(3)-Equivariant Robot Learning and Control: A Tutorial Surveycited by 8
  17. 2024Symmetry-aware Reinforcement Learning for Robotic Assembly under Partial Observability with a Soft Wristcited by 7
  18. 2025SE(3)-Equivariant Diffusion Policy in Spherical Fourier Spacecited by 7
  19. 2023Symmetric Replay Training: Enhancing Sample Efficiency in Deep Reinforcement Learning for Combinatorial Optimizationcited by 6
  20. 2023E(2)-Equivariant Graph Planning for Navigationcited by 6
  21. 2024MATCH POLICY: A Simple Pipeline from Point Cloud Registration to Manipulation Policiescited by 6
  22. 2025Constraint-Preserving Data Generation for Visuomotor Policy Learningcited by 6
  23. 2025Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetrycited by 6
  24. 2023SO(2)-Equivariant Downwash Models for Close Proximity Flightcited by 5
  25. 2024Advanced deep-reinforcement-learning methods for flow control: group-invariant and positional-encoding networks improve learning speed and qualitycited by 5
  26. 2025Latent Mixture of Symmetries for Sample-Efficient Dynamic Learningcited by 5
  27. 2022Equivariant Reinforcement Learning for Quadrotor UAVcited by 4
  28. 2023rm E(3)-Equivariant Actor-Critic Methods for Cooperative Multi-Agent Reinforcement Learningcited by 4
  29. 2023Learning Regularized Graphon Mean-Field Games with Unknown Graphonscited by 4
  30. 2024Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guaranteescited by 4
  31. 2025A Practical Guide for Incorporating Symmetry in Diffusion Policycited by 4
  32. 20253D Equivariant Visuomotor Policy Learning via Spherical Projectioncited by 4
  33. 2025EfficientFlow: Efficient Equivariant Flow Policy Learning for Embodied AIcited by 4
  34. 2023Equivariant MuZerocited by 3
  35. 2023Equivariant Data Augmentation for Generalization in Offline Reinforcement Learningcited by 3
  36. 2024Equivariant Ensembles and Regularization for Reinforcement Learning in Map-based Path Planningcited by 3
  37. 2024SiT: Symmetry-Invariant Transformers for Generalisation in Reinforcement Learningcited by 3
  38. 2025Symmetry-Guided Memory Augmentation for Efficient Locomotion Learningcited by 3

50 most cited of 79 All 79 (JSON)