# On Symmetry for Characterizing Agent Heterogeneity in Multi-Agent Systems

arXiv: https://arxiv.org/abs/2610.18538 · HTML: https://mlsanity.com/paper/2610.18538/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 15 of 15)

- [AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation](https://mlsanity.com/paper/2308.08155/) (2023)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [QTRAN: Learning to Factorize with Transformation for Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1905.05408/) (2019)
- [The Complexity of Decentralized Control of Markov Decision Processes](https://mlsanity.com/paper/1301.3836/) (2013)
- [Multi-agent Reinforcement Learning in Sequential Social Dilemmas](https://mlsanity.com/paper/1702.03037/) (2017)
- ["Other-Play" for Zero-Shot Coordination](https://mlsanity.com/paper/2003.02979/) (2020)
- [Universal Invariant and Equivariant Graph Neural Networks](https://mlsanity.com/paper/1905.04943/) (2019)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [MDP Homomorphic Networks: Group Symmetries in Reinforcement Learning](https://mlsanity.com/paper/2006.16908/) (2020)
- [Shapley Q-value: A Local Reward Approach to Solve Global Reward Games](https://mlsanity.com/paper/1907.05707/) (2019)
- [Multi-Agent Reinforcement Learning for Active Voltage Control on Power Distribution Networks](https://mlsanity.com/paper/2110.14300/) (2021)
- [A New Formalism, Method and Open Issues for Zero-Shot Coordination](https://mlsanity.com/paper/2106.06613/) (2021)
- [Policy Iteration for Decentralized Control of Markov Decision Processes](https://mlsanity.com/paper/1401.3460/) (2014)
- [Computing Game Symmetries and Equilibria That Respect Them](https://mlsanity.com/paper/2501.08905/) (2025)
- [Asymmetry underlies stability in power grids](https://mlsanity.com/paper/2103.10952/) (2021)

## Abstract (arXiv)

Understanding agent heterogeneity can inform the design of shared and agent-specific policy representations, however existing criteria provide no unified structural test. We study finite-horizon POSGs and define a type-compatible transformation as a policy-evaluation symmetry when complete policy evaluation commutes with it for every decentralized behavioral policy. Policy-evaluation symmetries form a group for which agent orbits define structural agent types. This classification does not depend on the particular policy chosen or the distribution of initial states. We prove that every componentwise environment automorphism is a policy-evaluation symmetry, but that the converse does not hold. Applying the framework to cooperative Dec-POMDPs shows that agents can belong to different structural types even when they share a common reward. For prescribed weighted reward aggregation, we derive an exact value identity and sufficient conditions for the resulting Dec-POMDP to inherit the policy-evaluation symmetries of the source POSG. Finally, we give sufficient conditions under which repeated model factorizations induce policy-evaluation symmetry, and show that preserving an optimal Boltzmann policy set neither implies nor follows from this symmetry in general.