用图结构分解多智能体约束问题,实现高效协同与可调权衡。
Coordination Graphs for Constrained Multi-Agent Reinforcement Learning

- 基于协调图与拉格朗日对偶,将联合策略拆分为成对区域学习
- 10智能体任务中生成优于基线的帕累托前沿,且无需重训练
- 适合大规模多智能体协同优化,尤其关注约束平衡的场景
受限多智能体强化学习(CMARL)面临两大挑战:联合动作空间随智能体数量指数增长,且额外约束使智能体间耦合关系难以仅靠奖励结构捕捉。本文提出CG-CMARL框架,通过结合协调图与拉格朗日对偶性,将联合问题分解为成对区域,每个区域由一组共享的Q函数处理,包括一个主目标和每个约束对应的函数,使学习模型数量与智能体数无关。执行时,采用最大和消息传递在因子图上协调动作,同时拉格朗日乘子控制目标与约束的权衡,使单一训练模型即可生成帕累托前沿而无需重新训练。我们在合作导航任务上验证该方法,团队规模达10个智能体,需满足成对约束并抵达目标位置,结果表明该方法生成的帕累托前沿全面超越固定奖励加权基线,且在集中式方法失效的大规模场景仍具可行性。理论分析提供温和条件下的收敛保证,并给出可分解的组合误差界,各部分可追溯至具体设计选择并独立调控。
原文摘要 · Abstract (English)
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.
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