Train Locally, Learn Together: Distributed Multi-Agent Learning via ADMM

Multi-agent systems (MAS) can outperform individual language-model agents by combining specialized roles, diverse reasoning processes, and collaborative decision-making. However, collaborative MAS training is typically centralized, requiring a common trainer to aggregate role-local trajectories and learning signals and maintain model and optimization states. This motivates a distributed multi-agent learning paradigm in which agents improve system-level capabilities through role-local learning and decentralized communication, paving the way toward scalable, resilient, and self-organizing MAS. To this end, we introduce, to the best of our knowledge, the first optimization-grounded framework for distributed MAS training based on consensus alternating direction method of multipliers (ADMM). We formulate collaborative MAS learning as a consensus-constrained finite-sum optimization problem, naturally lending itself to distributed optimization via ADMM. The proposed approach alternates role-local learning with inter-agent consensus using distributed communication protocols such as ring all-reduce, enabling joint optimization while keeping each agent's data and training state local. We evaluate our framework on distributed safety alignment and general reasoning tasks. ADMM reduces HarmBench ASR by up to 26.4% points under compromised-agent settings, while achieving reasoning gains comparable to centralized training. These results show that distributed MAS training retains the benefits of centralized joint optimization without requiring a centralized trainer.