On Symmetry for Characterizing Agent Heterogeneity in Multi-Agent Systems

Decentralised partially observable Markov decision processes (DecPOMDPs) provide a general framework for modelling multi-agent decision making under uncertainty. However, DecPOMDPs are known to suffer from exponential complexity in the number of agents. One way to combat this intractability in agent numbers is to look at partitions of agents that exhibit a form of symmetry among agents, allowing for a compact encoding by counting. However, a challenge arises as the policy space explodes, even though the model complexity and evaluation cost reduce to a polynomial dependence. In this paper, we redirect our focus from counting agents to counting policies, which actually enables tractability in agent numbers for so called policy-counted DecPOMDPs. Further, we present policy-counted dynamic programming using the compact representation to solve policy-counted DecPOMDPs efficiently.

Multi-agent systems (MAS) leverage interactions between agents to perform complex tasks. Despite their success, we show that these interactions can also lead to homogenization, i.e., agents converging to similar behaviors. Homogenization in MAS can reduce agent diversity and reinforce shared failures. In this paper, we operationalize homogenization using three metrics: conformity to the majority, polarization towards extremes, and growing inertia against changes over subsequent interactions. We evaluate homogenization in MAS for code generation, hiring, and scientific peer review. Across these tasks, we show that homogenization translates to concrete downstream risks: in code generation, it hides and amplifies correlated errors which can create systemic vulnerabilities; in hiring, it allows the influence of biased agents to persist long after their removal; and in peer review, it creates uneven evaluation standards across research areas. Our results establish homogenization as a failure mode of MAS, demonstrating that MAS evaluations must move beyond aggregate performance to carefully analyze interaction dynamics. Finally, we show that simple approaches to increase diversity---leveraging sampling stochasticity and mixed-models MAS---fail to reduce homogenization risks, highlighting the need for strategies to effectively leverage agent diversity.

Centralized training with decentralized execution (CTDE) is a standard framework for cooperative multi-agent policy-gradient reinforcement learning, allowing agents to learn from joint information while acting from local observations. Ratio-based trust-region methods such as Multi-Agent Proximal Policy Optimization (MAPPO) and Multi-Agent Simple Policy Optimization (MASPO) update decentralized actors using per-agent probability ratios weighted by joint advantage estimates. Teammate non-stationarity increases the variance of these advantages, which in turn increases the variance in the local ratio updates. This exposes two method-specific failure modes: MAPPO's additive clipping removes gradients for outlier samples and weakens recovery from policy drift, while MASPO's soft quadratic penalty can allow probability collapse. We introduce Multi-Agent Ratio Symmetry (MARS), a novel policy optimization objective that replaces these additive ratio-based trust-region mechanisms with a multiplicatively symmetric geometric barrier. MARS preserves corrective gradients while assigning unbounded cost as probability ratios approach zero. Across 47 tasks spanning eight multi-agent environments, including novel JAX benchmarks PaxMen and AeroJAX, MARS matches or exceeds MAPPO and MASPO in aggregate environment-level performance. Ablations show that these gains arise from the geometry of the symmetric barrier rather than from flexible trust-region boundaries alone.