# Equivariant Networks for Zero-Shot Coordination

arXiv: https://arxiv.org/abs/2210.12124 · HTML: https://mlsanity.com/paper/2210.12124/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 60 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Value-Decomposition Networks For Cooperative Multi-Agent Learning](https://mlsanity.com/paper/1706.05296/) (2017)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Learning Multiagent Communication with Backpropagation](https://mlsanity.com/paper/1605.07736/) (2016)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- ["Other-Play" for Zero-Shot Coordination](https://mlsanity.com/paper/2003.02979/) (2020)
- [The Hanabi Challenge: A New Frontier for AI Research](https://mlsanity.com/paper/1902.00506/) (2019)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [Graph Convolutional Reinforcement Learning](https://mlsanity.com/paper/1810.09202/) (2018)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Deep Scale-spaces: Equivariance Over Scale](https://mlsanity.com/paper/1905.11697/) (2019)
- [Deep Coordination Graphs](https://mlsanity.com/paper/1910.00091/) (2019)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [Off-Belief Learning](https://mlsanity.com/paper/2103.04000/) (2021)
- [Symmetry-Aware Actor-Critic for 3D Molecular Design](https://mlsanity.com/paper/2011.12747/) (2020)
- [Sample Efficient Grasp Learning Using Equivariant Models](https://mlsanity.com/paper/2202.09468/) (2022)
- [Simplified Action Decoder for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1912.02288/) (2019)
- [PIC: Permutation Invariant Critic for Multi-Agent Deep Reinforcement Learning](https://mlsanity.com/paper/1911.00025/) (2019)
- [3D G-CNNs for Pulmonary Nodule Detection](https://mlsanity.com/paper/1804.04656/) (2018)
- [Continuous Coordination As a Realistic Scenario for Lifelong Learning](https://mlsanity.com/paper/2103.03216/) (2021)
- [K-level Reasoning for Zero-Shot Coordination in Hanabi](https://mlsanity.com/paper/2207.07166/) (2022)
- [On the Critical Role of Conventions in Adaptive Human-AI Collaboration](https://mlsanity.com/paper/2104.02871/) (2021)
- [Multi-Agent MDP Homomorphic Networks](https://mlsanity.com/paper/2110.04495/) (2021)
- [Group Equivariant Deep Reinforcement Learning](https://mlsanity.com/paper/2007.03437/) (2020)

## Built on by (most cited first, 16 of 16)

- [Secret Collusion among AI Agents: Multi-Agent Deception via Steganography](https://mlsanity.com/paper/2402.07510/) (2024)
- [EDGI: Equivariant Diffusion for Planning with Embodied Agents](https://mlsanity.com/paper/2303.12410/) (2023)
- [Equivariant Reinforcement Learning under Partial Observability](https://mlsanity.com/paper/2408.14336/) (2024)
- [Efficient Equivariant Transfer Learning from Pretrained Models](https://mlsanity.com/paper/2305.09900/) (2023)
- [Who Needs to Know? Minimal Knowledge for Optimal Coordination](https://mlsanity.com/paper/2306.09309/) (2023)
- [Equivariant MuZero](https://mlsanity.com/paper/2302.04798/) (2023)
- [The Yokai Learning Environment: Tracking Beliefs Over Space and Time](https://mlsanity.com/paper/2508.12480/) (2025)
- [High entropy leads to symmetry-equivariant policies in Dec-POMDPs](https://mlsanity.com/paper/2511.22581/) (2025)
- [Symmetry-Breaking Augmentations for Ad Hoc Teamwork](https://mlsanity.com/paper/2402.09984/) (2024)
- [Improving Controller Generalization with Dimensionless Markov Decision Processes](https://mlsanity.com/paper/2504.10006/) (2025)
- [Robust and Diverse Multi-Agent Learning via Rational Policy Gradient](https://mlsanity.com/paper/2511.09535/) (2025)
- [Training Generalizable Collaborative Agents via Strategic Risk Aversion](https://mlsanity.com/paper/2602.21515/) (2026)
- [Shaping Zero-Shot Coordination via State Blocking](https://mlsanity.com/paper/2605.11688/) (2026)
- [Is Inter-Seed Cross-Play Enough? Evaluating the Robustness of Zero-Shot Coordination Algorithms to Implementation Details](https://mlsanity.com/paper/2608.03644/) (2026)
- [Reinforcement Learning Using known Invariances](https://mlsanity.com/paper/2511.03473/) (2025)
- [Efficient Reinforcement Learning for Zero-Shot Coordination in Evolving Games](https://mlsanity.com/paper/2511.11083/) (2025)

## Abstract (arXiv)

Successful coordination in Dec-POMDPs requires agents to adopt robust strategies and interpretable styles of play for their partner. A common failure mode is symmetry breaking, when agents arbitrarily converge on one out of many equivalent but mutually incompatible policies. Commonly these examples include partial observability, e.g. waving your right hand vs. left hand to convey a covert message. In this paper, we present a novel equivariant network architecture for use in Dec-POMDPs that effectively leverages environmental symmetry for improving zero-shot coordination, doing so more effectively than prior methods. Our method also acts as a ``coordination-improvement operator'' for generic, pre-trained policies, and thus may be applied at test-time in conjunction with any self-play algorithm. We provide theoretical guarantees of our work and test on the AI benchmark task of Hanabi, where we demonstrate our methods outperforming other symmetry-aware baselines in zero-shot coordination, as well as able to improve the coordination ability of a variety of pre-trained policies. In particular, we show our method can be used to improve on the state of the art for zero-shot coordination on the Hanabi benchmark.