Learning Large-Scale Competitive Team Behaviors with Mean-Field Interactions

Coordinating large populations of interacting agents is a central challenge in multi-agent reinforcement learning (MARL), where the size of the joint state-action space scales exponentially with the number of agents. Mean-field methods alleviate this burden by aggregating agent interactions, but these approaches assume homogeneous interactions. Recent graphon-based frameworks capture heterogeneity, but are computationally expensive as the number of agents grows. Therefore, we introduce $\texttt{GMFS}$, a $\textbf{G}$raphon $\textbf{M}$ean-$\textbf{F}$ield $\textbf{S}$ubsampling framework for scalable cooperative MARL with heterogeneous agent interactions. By subsampling $κ$ agents according to interaction strength, we approximate the graphon-weighted mean-field and learn a policy with sample complexity $\mathrm{poly}(κ)$ and optimality gap $O(1/\sqrtκ)$. We verify our theory with numerical simulations in robotic coordination, showing that $\texttt{GMFS}$ achieves near-optimal performance.

Diffusion-based planning has achieved strong results in single-agent offline reinforcement learning, yet scaling to many-agent systems remains intractable due to the curse of dimensionality in the joint trajectory space. We introduce MF-Diffuser, a framework that lifts trajectory planning to the Wasserstein space of trajectory distributions, where the propagation of chaos ensures a small representative subset of agents captures the full population dynamics. Our approach features a value-weighted chaotic entropy objective that reconciles generative fidelity with return maximization, and a hierarchical coarse-to-fine strategy that progressively grows the agent population during denoising. We establish end-to-end suboptimality bounds with four interpretable terms, revealing that mean-field approximation error scales as $O(H^2/\sqrt{N})$ while offline distribution shift provably does not grow with population size $N$, and prove the generated policy is an approximate mean-field Nash equilibrium with explicit convergence guarantees. Experiments on three mean-field RL benchmarks -- spanning stage games, sequential dynamics, and adversarial team competition -- show MF-Diffuser achieves the best return in the majority of settings, with the largest gains on suboptimal offline data and at extreme scales ($N \geq 10^3$).

Modern multi-agent systems are increasingly deployed at scale over large populations of agents in settings such as ad-auctions, traffic routing, and recommendation systems. The dominant approach in such settings is to optimize each agent's policy independently, treating the other agents as part of a fixed single-agent environment rather than modeling the population dynamics. In many large-population systems, the dynamics depend on an aggregate summary of the population rather than the identity of any individual. Mean-field RL exploits such structure, providing a principled framework that models each agent's environment as an explicit function of the population distribution. However, in large state-action spaces or high-dimensional control problems, modeling the population distribution is itself intractable. How can we design a scalable framework for high-dimensional control problems with large populations? This work explores this question from the perspective of representation learning. We introduce a mean-field RL framework in which the rewards and transition dynamics depend on the population only through an unknown low-dimensional aggregate statistic. We then study this framework in the offline setting and design a provable approach that learns a near-optimal policy by learning a low-dimensional representation. Motivated by real-life supply-chain optimization problems, we design a one-step routing game to test the hypothesis that learning a low-dimensional population representation improves reward prediction and Nash gap estimation relative to baselines that don't exploit this structure. We show that under a fixed neural-network parameter count and optimization budget, learning a low-dimensional population representation improves reward prediction and the equilibrium quality of the resulting policies.