# SO(2)-Equivariant Reinforcement Learning

arXiv: https://arxiv.org/abs/2203.04439 · HTML: https://mlsanity.com/paper/2203.04439/

## Key facts

- Cited by 84 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2022.

## Built on by (most cited first, 30 of 84)

- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024)
- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [Does equivariance matter at scale?](https://mlsanity.com/paper/2410.23179/) (2024)
- [EDGI: Equivariant Diffusion for Planning with Embodied Agents](https://mlsanity.com/paper/2303.12410/) (2023)
- [The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry](https://mlsanity.com/paper/2211.09231/) (2022)
- [Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3D](https://mlsanity.com/paper/2401.12046/) (2024)
- [Symmetry Considerations for Learning Task Symmetric Robot Policies](https://mlsanity.com/paper/2403.04359/) (2024)
- [Continuous MDP Homomorphisms and Homomorphic Policy Gradient](https://mlsanity.com/paper/2209.07364/) (2022)
- [Leveraging Symmetry in RL-based Legged Locomotion Control](https://mlsanity.com/paper/2403.17320/) (2024)
- [SEIL: Simulation-augmented Equivariant Imitation Learning](https://mlsanity.com/paper/2211.00194/) (2022)
- [A General Theory of Correct, Incorrect, and Extrinsic Equivariance](https://mlsanity.com/paper/2303.04745/) (2023)
- [Learning to Extrapolate: A Transductive Approach](https://mlsanity.com/paper/2304.14329/) (2023)
- [Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policies](https://mlsanity.com/paper/2406.11740/) (2024)
- [Equivariant Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/2408.14336/) (2024)
- [Equivariant Networks for Zero-Shot Coordination](https://mlsanity.com/paper/2210.12124/) (2022)
- [One-shot Imitation Learning via Interaction Warping](https://mlsanity.com/paper/2306.12392/) (2023)
- [Unsupervised Learning of Equivariant Structure from Sequences](https://mlsanity.com/paper/2210.05972/) (2022)
- [Relational Reasoning via Set Transformers: Provable Efficiency and Applications to MARL](https://mlsanity.com/paper/2209.09845/) (2022)
- [On Robot Grasp Learning Using Equivariant Models](https://mlsanity.com/paper/2306.06489/) (2023)
- [RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation](https://mlsanity.com/paper/2403.19460/) (2024)
- [Continual Vision-based Reinforcement Learning with Group Symmetries](https://mlsanity.com/paper/2210.12301/) (2022)
- [Geometry-aware RL for Manipulation of Varying Shapes and Deformable Objects](https://mlsanity.com/paper/2502.07005/) (2025)
- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- [Policy Gradient Methods in the Presence of Symmetries and State Abstractions](https://mlsanity.com/paper/2305.05666/) (2023)
- [Sample Efficient Reinforcement Learning in Mixed Systems through Augmented Samples and Its Applications to Queueing Networks](https://mlsanity.com/paper/2305.16483/) (2023)
- [ESP: Exploiting Symmetry Prior for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2307.16186/) (2023)
- [Symmetry-aware Reinforcement Learning for Robotic Assembly under Partial Observability with a Soft Wrist](https://mlsanity.com/paper/2402.18002/) (2024)
- [Approximate Equivariance in Reinforcement Learning](https://mlsanity.com/paper/2411.04225/) (2024)

## 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.