# Permutation Robustness Is Not Enough: Action Collapse in Multi-Agent Transformer Policies

arXiv: https://arxiv.org/abs/2610.02848 · HTML: https://mlsanity.com/paper/2610.02848/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 20 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (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)
- [QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1803.11485/) (2018)
- [Value-Decomposition Networks For Cooperative Multi-Agent Learning](https://mlsanity.com/paper/1706.05296/) (2017)
- [Emergent Tool Use From Multi-Agent Autocurricula](https://mlsanity.com/paper/1909.07528/) (2019)
- [Emergence of Grounded Compositional Language in Multi-Agent Populations](https://mlsanity.com/paper/1703.04908/) (2017)
- [Actor-Attention-Critic for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1810.02912/) (2018)
- [PettingZoo: Gym for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2009.14471/) (2020)
- [MAVEN: Multi-Agent Variational Exploration](https://mlsanity.com/paper/1910.07483/) (2019)
- [Learning Attentional Communication for Multi-Agent Cooperation](https://mlsanity.com/paper/1805.07733/) (2018)

## Abstract (arXiv)

Transformer policies are attractive for multi-agent robot learning because self-attention can model interactions among agents. However, multi-agent teams are unordered, while transformers typically process agents as ordered token sequences. We study how this mismatch affects cooperative navigation policies under agent-order permutations. Our results show that low permutation error alone can be misleading: policies may appear robust simply because all agents choose the same action. We therefore evaluate policies using both permutation-consistency metrics and action-collapse diagnostics, including action diversity, same-action fraction, and maximum action frequency. A PPO-ID baseline yields non-collapsed behavior but remains order-sensitive, while strong equivariance regularization can still induce homogeneous behavior. A weak equivariance penalty improves the robustness while preserving more diverse actions for teams with (N=3) agents, whereas teams with (N=4) agents require substantially smaller regularization weights. These findings suggest that multi-agent transformer policies should be evaluated not only by return and permutation robustness, but also by whether they maintain non-collapsed, differentiated multi-agent behavior.