SLRC: Structured Low-Rank Coupling for One-Round Communication in Cooperative Multi-Agent Reinforcement Learning

Efficient coordination under partial observability remains a central challenge in multi-agent reinforcement learning. Communication supplements local observations, while multi-round exchanges enable agents to refine their responses using updated peer information. However, these exchanges introduce sequential dependencies across rounds. Inspired by this refinement process, we introduce SLRC (**S**tructured **L**ow-**R**ank **C**oupling), a one-round communication framework for cooperative MARL. SLRC adopts a structured affine response model that separates agent-specific transformations from rank-$r$ interaction dependencies. Each agent encodes its contribution into a compact packet of dimension $r^2+r$. After one logical exchange, receivers aggregate available packets and solve an $r$-dimensional linear system to locally infer the outcome of iterative refinement within the learned response model. Our analysis establishes exact decoding of the model-defined coupled response and its equivalence to the limit of iterative refinement under contraction. Experiments show that SLRC achieves the highest performance among the evaluated methods across 13 Cooperative Navigation, Predator Prey, and SMACv2 scenarios and remains effective under field-of-view (FoV) constraints. Sparse-reward Hallway tasks reveal a limitation, while rank analyses characterize the trade-off between interaction capacity and message payload. SLRC offers a new perspective on cooperative MARL communication by shifting from repeated exchanges to structured interaction inference within one round.