# Group Equivariant Deep Reinforcement Learning

arXiv: https://arxiv.org/abs/2007.03437 · HTML: https://mlsanity.com/paper/2007.03437/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 24 of 24)

- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [Equivariant Adaptation of Large Pretrained Models](https://mlsanity.com/paper/2310.01647/) (2023)
- [The Surprising Effectiveness of Equivariant Models in Domains with Latent Symmetry](https://mlsanity.com/paper/2211.09231/) (2022)
- [Leveraging Symmetry in RL-based Legged Locomotion Control](https://mlsanity.com/paper/2403.17320/) (2024)
- [Self-Interpretable Model with TransformationEquivariant Interpretation](https://mlsanity.com/paper/2111.04927/) (2021)
- [Unsupervised Representation Learning in Deep Reinforcement Learning: A Review](https://mlsanity.com/paper/2208.14226/) (2022)
- [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)
- [On Robot Grasp Learning Using Equivariant Models](https://mlsanity.com/paper/2306.06489/) (2023)
- [Sample Efficient Reinforcement Learning in Mixed Systems through Augmented Samples and Its Applications to Queueing Networks](https://mlsanity.com/paper/2305.16483/) (2023)
- [Approximate Equivariance in Reinforcement Learning](https://mlsanity.com/paper/2411.04225/) (2024)
- [Improved Canonicalization for Model Agnostic Equivariance](https://mlsanity.com/paper/2405.14089/) (2024)
- [Integrating Symmetry into Differentiable Planning with Steerable Convolutions](https://mlsanity.com/paper/2206.03674/) (2022)
- [E(2)-Equivariant Graph Planning for Navigation](https://mlsanity.com/paper/2309.13043/) (2023)
- [Addressing imperfect symmetry: A novel symmetry-learning actor-critic extension](https://mlsanity.com/paper/2309.02711/) (2023)
- [Equivariant Offline Reinforcement Learning](https://mlsanity.com/paper/2406.13961/) (2024)
- [3D Equivariant Visuomotor Policy Learning via Spherical Projection](https://mlsanity.com/paper/2505.16969/) (2025)
- [ReF -- Rotation Equivariant Features for Local Feature Matching](https://mlsanity.com/paper/2203.05206/) (2022)
- [Coordinated Humanoid Robot Locomotion with Symmetry Equivariant Reinforcement Learning Policy](https://mlsanity.com/paper/2508.01247/) (2025)
- [Can Euclidean Symmetry be Leveraged in Reinforcement Learning and Planning?](https://mlsanity.com/paper/2307.08226/) (2023)
- [Symmetries-enhanced Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2501.01136/) (2025)
- [Learning Abstract World Models with a Group-Structured Latent Space](https://mlsanity.com/paper/2506.01529/) (2025)
- [Learning Geometric Representations of Objects via Interaction](https://mlsanity.com/paper/2309.05346/) (2023)
- [SymVD: Symmetric Vision Language Action Distillation for Robot Manipulation](https://mlsanity.com/paper/2608.29828/) (2026)

## Abstract (arXiv)

In Reinforcement Learning (RL), Convolutional Neural Networks(CNNs) have been successfully applied as function approximators in Deep Q-Learning algorithms, which seek to learn action-value functions and policies in various environments. However, to date, there has been little work on the learning of symmetry-transformation equivariant representations of the input environment state. In this paper, we propose the use of Equivariant CNNs to train RL agents and study their inductive bias for transformation equivariant Q-value approximation. We demonstrate that equivariant architectures can dramatically enhance the performance and sample efficiency of RL agents in a highly symmetric environment while requiring fewer parameters. Additionally, we show that they are robust to changes in the environment caused by affine transformations.