# Subequivariant Reinforcement Learning in 3D Multi-Entity Physical Environments

arXiv: https://arxiv.org/abs/2407.12505 · HTML: https://mlsanity.com/paper/2407.12505/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 49 of its 67 references that are in the map.
- First posted on arXiv 17 Jul 2024.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 30 of 49)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [Counterfactual Multi-Agent Policy Gradients](https://mlsanity.com/paper/1705.08926/) (2017)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1803.11485/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [The StarCraft Multi-Agent Challenge](https://mlsanity.com/paper/1902.04043/) (2019)
- [Learning to Communicate with Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1605.06676/) (2016)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Actor-Attention-Critic for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1810.02912/) (2018)
- [The Complexity of Decentralized Control of Markov Decision Processes](https://mlsanity.com/paper/1301.3836/) (2013)
- [Trust Region Policy Optimisation in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2109.11251/) (2021)
- [Multi-Agent Reinforcement Learning is a Sequence Modeling Problem](https://mlsanity.com/paper/2205.14953/) (2022)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Learning Modular Neural Network Policies for Multi-Task and Multi-Robot Transfer](https://mlsanity.com/paper/1609.07088/) (2016)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [SMACv2: An Improved Benchmark for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2212.07489/) (2022)
- [One Policy to Control Them All: Shared Modular Policies for Agent-Agnostic Control](https://mlsanity.com/paper/2007.04976/) (2020)
- [Emergent Complexity via Multi-Agent Competition](https://mlsanity.com/paper/1710.03748/) (2017)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [MetaMorph: Learning Universal Controllers with Transformers](https://mlsanity.com/paper/2203.11931/) (2022)
- [From Motor Control to Team Play in Simulated Humanoid Football](https://mlsanity.com/paper/2105.12196/) (2021)

## Built on by (most cited first, 2 of 2)

- [Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?](https://mlsanity.com/paper/2410.11443/) (2024)
- [Efficient Morphology-Control Co-Design via Stackelberg Proximal Policy Optimization](https://mlsanity.com/paper/2603.15388/) (2026)

## Abstract (arXiv)

Learning policies for multi-entity systems in 3D environments is far more complicated against single-entity scenarios, due to the exponential expansion of the global state space as the number of entities increases. One potential solution of alleviating the exponential complexity is dividing the global space into independent local views that are invariant to transformations including translations and rotations. To this end, this paper proposes Subequivariant Hierarchical Neural Networks (SHNN) to facilitate multi-entity policy learning. In particular, SHNN first dynamically decouples the global space into local entity-level graphs via task assignment. Second, it leverages subequivariant message passing over the local entity-level graphs to devise local reference frames, remarkably compressing the representation redundancy, particularly in gravity-affected environments. Furthermore, to overcome the limitations of existing benchmarks in capturing the subtleties of multi-entity systems under the Euclidean symmetry, we propose the Multi-entity Benchmark (MEBEN), a new suite of environments tailored for exploring a wide range of multi-entity reinforcement learning. Extensive experiments demonstrate significant advancements of SHNN on the proposed benchmarks compared to existing methods. Comprehensive ablations are conducted to verify the indispensability of task assignment and subequivariance.