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MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning

arXiv 2006.16908 ↗First posted 30 Jun 2020cs.LG stat.MLcited by 133

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Abstract (arXiv)

This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep reinforcement learning do not usually exploit knowledge about such structure. By building this prior knowledge into policy and value networks using an equivariance constraint, we can reduce the size of the solution space. We specifically focus on group-structured symmetries (invertible transformations). Additionally, we introduce an easy method for constructing equivariant network layers numerically, so the system designer need not solve the constraints by hand, as is typically done. We construct MDP homomorphic MLPs and CNNs that are equivariant under either a group of reflections or rotations. We show that such networks converge faster than unstructured baselines on CartPole, a grid world and Pong.

Key facts. Cited by 133 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Jun 2020.

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Citing papers per year: 2021: 17; 2022: 26; 2023: 30; 2024: 24; 2025: 18; 2026: 18.

133 papers.

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  1. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  2. 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
  3. 2022Equivariance with Learned Canonicalization Functionscited by 106
  4. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 74
  5. 2023For SALE: State-Action Representation Learning for Deep Reinforcement Learningcited by 73
  6. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  7. 2021Towards Robust Bisimulation Metric Learningcited by 49
  8. 2022Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximationscited by 42
  9. 2025Towards General-Purpose Model-Free Reinforcement Learningcited by 40
  10. 2021Return-Based Contrastive Representation Learning for Reinforcement Learningcited by 36
  11. 2022Trustworthy Reinforcement Learning Against Intrinsic Vulnerabilities: Robustness, Safety, and Generalizabilitycited by 32
  12. 2022The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetrycited by 32
38 more
  1. 2021Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamicscited by 27
  2. 2021A Dataset Perspective on Offline Reinforcement Learningcited by 27
  3. 2022Symmetry-Based Representations for Artificial and Biological General Intelligencecited by 26
  4. 2023Learning Probabilistic Symmetrization for Architecture Agnostic Equivariancecited by 25
  5. 2021Multi-Agent MDP Homomorphic Networkscited by 24
  6. 2022Continuous MDP Homomorphisms and Homomorphic Policy Gradientcited by 24
  7. 2024Cross-Domain Policy Adaptation by Capturing Representation Mismatchcited by 24
  8. 2023Learning Layer-wise Equivariances Automatically using Gradientscited by 23
  9. 2022Toward Compositional Generalization in Object-Oriented World Modelingcited by 22
  10. 2022Equi-Tuning: Group Equivariant Fine-Tuning of Pretrained Modelscited by 22
  11. 2022Maximum Class Separation as Inductive Bias in One Matrixcited by 21
  12. 2022Homomorphism Autoencoder -- Learning Group Structured Representations from Observed Transitionscited by 18
  13. 2022Unsupervised Representation Learning in Deep Reinforcement Learning: A Reviewcited by 18
  14. 2023A General Theory of Correct, Incorrect, and Extrinsic Equivariancecited by 18
  15. 2024Symmetry Considerations for Learning Task Symmetric Robot Policiescited by 18
  16. 2024One-Shot Imitation Learning with Invariance Matching for Robotic Manipulationcited by 18
  17. 2024Equivariant Reinforcement Learning under Partial Observabilitycited by 17
  18. 2022Equivariant Networks for Zero-Shot Coordinationcited by 16
  19. 2023Structure in Deep Reinforcement Learning: A Survey and Open Problemscited by 16
  20. 2022Unsupervised Learning of Equivariant Structure from Sequencescited by 15
  21. 2023Neurosymbolic Grounding for Compositional World Modelscited by 14
  22. 2023Symmetry-Aware Robot Design with Structured Subgroupscited by 13
  23. 2023On Robot Grasp Learning Using Equivariant Modelscited by 12
  24. 2023Efficient Equivariant Transfer Learning from Pretrained Modelscited by 11
  25. 2023Flow Factorized Representation Learningcited by 11
  26. 2022Continual Vision-based Reinforcement Learning with Group Symmetriescited by 10
  27. 2023Subequivariant Graph Reinforcement Learning in 3D Environmentscited by 10
  28. 2023Guided Data Augmentation for Offline Reinforcement Learning and Imitation Learningcited by 10
  29. 2025Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objectscited by 10
  30. 2023Sample Efficient Reinforcement Learning in Mixed Systems through Augmented Samples and Its Applications to Queueing Networkscited by 9
  31. 2023ESP: Exploiting Symmetry Prior for Multi-Agent Reinforcement Learningcited by 9
  32. 2024Morphological Symmetries in Roboticscited by 9
  33. 2024Boosting Sample Efficiency and Generalization in Multi-agent Reinforcement Learning via Equivariancecited by 9
  34. 2024Approximate Equivariance in Reinforcement Learningcited by 9
  35. 2021Neural Networks for Learning Counterfactual G-Invariances from Single Environmentscited by 8
  36. 2022Learning from Symmetry: Meta-Reinforcement Learning with Symmetrical Behaviors and Language Instructionscited by 8
  37. 2023Policy Gradient Methods in the Presence of Symmetries and State Abstractionscited by 8
  38. 2025SE(3)-Equivariant Robot Learning and Control: A Tutorial Surveycited by 8

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