Distributed blackbox consensus optimization is a fundamental problem in multi-agent systems, where agents must improve a global objective using only local objective queries and limited neighbor communication. Existing methods largely rely on handcrafted update rules and static cooperation patterns, which often struggle to balance local adaptation, global coordination, and communication efficiency in heterogeneous nonconvex environments. In this paper, we take an initial step toward trajectory-driven self-design for distributed black-box consensus optimization. We first redesign the agent-level swarm dynamics with an adaptive internal mechanism tailored to decentralized consensus settings, improving the balance between exploration, convergence, and local escape. Built on top of this adaptive execution layer, we propose Learning to Act and Cooperate (LACMAS), a trajectorydriven framework in which large language models provide sparse highlevel guidance for shaping both agentinternal action behaviors and agentexternal cooperation patterns from historical optimization trajectories. We further introduce a phased cognitive scheduling strategy to activate different forms of adaptation in a resource-aware manner. Experiments on standard distributed black-box benchmarks and real-world distributed tasks show that LAC-MAS consistently improves solution quality, convergence efficiency, and communication efficiency over strong baselines, suggesting a practical route from handcrafted distributed coordination toward self-designing multi-agent optimization systems.

翻译：分布式黑箱共识优化是多智能体系统中的基本问题，要求各智能体仅通过局部目标函数查询和有限邻域通信来提升全局目标。现有方法主要依赖人工设计的更新规则和静态协作模式，在异构非凸环境中往往难以平衡局部自适应、全局协调与通信效率。本文首次探索面向分布式黑箱共识优化的轨迹驱动型自设计方法。我们首先针对分布式共识场景，为智能体级群体动力学设计带自适应内部机制的改进方案，以增强探索、收敛与局部逃逸之间的平衡。基于该自适应执行层，我们提出学习与协作框架（LAC-MAS），该轨迹驱动型框架利用大语言模型从历史优化轨迹中提供稀疏高层指导，以塑造智能体内部行为与外部协作模式。进一步地，我们引入分阶段认知调度策略，以资源感知方式激活不同形式的自适应机制。在标准分布式黑箱基准测试和实际分布式任务上的实验表明，LAC-MAS在解质量、收敛效率和通信效率上均稳定优于强基线方法，为从人工设计型分布式协作迈向自设计型多智能体优化系统提供了可行路径。