Learning Multi-Agent Coordination via Sheaf-ADMM

Distributed optimization is a highly scalable and structurally transparent technique to solve multi-agent robotics problems; however, such methods often suffer from the need for highly-specialized, problem-specific hyperparameter tunings. In this work, we propose Deep Coordinator, a deep-unfolding framework that learns to dynamically adjust the hyperparameters of ADMM-DDP, a popular distributed solver for robotics tasks, at solve-time in response to optimizer performance. Our architecture consists of unrolling a fixed number of ADMM-DDP iterations into a neural network with learnable functions between layers mapping the optimizer state to the next hyperparameters. To the best of our knowledge, Deep Coordinator is the first deep-unfolding framework to adapt the penalty parameters of a non-convex optimizer at solve-time; we show that the mainstream supervised approach can yield degenerate solutions when training such models, and propose an unsupervised learning scheme. On simulations with fleets of cars and quadrotors, Deep Coordinator produces trajectories of comparable quality 6.18-9.44x faster than conventional solvers. Furthermore, Deep Coordinator retains its performance benefits when deployed to systems up to 8x larger than trained on.

As large language model (LLM)-based multi-agent systems scale to handle increasingly complex tasks, balancing structural stability and dynamic adaptability becomes increasingly challenging. Existing systems typically adopt either structure-centric methods, committing to structures determined upfront that limit fine-grained control, or orchestration-centric methods, adapting decisions dynamically while leaving coordination structure implicit and unstable. To address this challenge, we revisit multi-agent coordination from a probabilistic perspective, casting it as posterior inference over the joint distribution of structure and orchestration. We introduce MACA, an automated coordination framework that learns a task- and budget-conditioned structural prior over agent participation and interactions. This prior guides a policy-based orchestration as an approximation to posterior inference, enabling efficient solutions with fine-grained control. Across benchmarks, MACA outperforms adaptive multi-agent baselines by an average of 8.42% while using 43.19% fewer tokens. Further investigation reveals that joint adaptation of structure and orchestration suppresses redundant interactions, converging coordination toward task-effective execution.

Constrained Multi-agent reinforcement learning (CMARL) faces two intertwined challenges: the joint action space grows exponentially with the number of agents, and additional requirements couple agents in ways that reward structure alone does not capture. We introduce Coordination Graphs for Constrained Multi-Agent Reinforcement Learning (CG-CMARL), a framework that addresses both challenges by combining coordination graphs with Lagrangian duality. The system decomposes the joint problem into pairwise regions, each served by a set of shared Q-functions, one for the primary objective and one for each of the constraints, so that the number of learned models is independent of the number of agents. At execution time, Max-Sum message passing coordinates actions across the factor graph, while a Lagrangian multiplier controls the objective--constraint tradeoff, allowing a single trained model to trace a Pareto front without retraining. We provide convergence guarantees under mild conditions, together with a compositional error bound that decomposes into separate interpretable sources, each traceable to a specific design choice and independently controllable. Experiments on cooperative navigation tasks (where teams of up to 10 agents must coordinate to reach target positions while satisfying pairwise constraints) show that our method produces Pareto fronts dominating established baselines trained at fixed reward-shaping ratios, while scaling to team sizes where centralized approaches become intractable.