有限理性下人机协同的图设计：随机块模型的最优性
Graphon Design for Human-Machine Coordination under Bounded Rationality: Optimality of Stochastic Block Models
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中文总结 AI 辅助
本文针对有限理性下异质智能体的协同问题，采用平均场方法将图优化问题提升至图空间，证明双峰理性系统的最优图可在随机块模型集合中搜索，并提出注水算法求解局部最优图以规避组合复杂性。
中文摘要 AI 辅助
协同是多智能体系统的理想特性，涵盖机器人群到社会经济网络等场景。本文关注促进异质智能体（如机器与人类）在猎鹿博弈中的协同。模型中智能体表现出不同程度的有限理性，导致学习与决策过程中存在不确定性和犯错倾向。本文解决在上述约束下设计网络拓扑以最大化全局协同度量的问题。由于在有限图的离散空间优化通常计算上不可行，本文采用平均场方法将问题提升至图空间。在该框架内，分析遵循logit学习动态的智能体，运用变分法证明，对于具有双峰理性轮廓的系统，只需在随机块模型集合中搜索最优图。随后提出注水算法以寻找局部最优图，再从优化后的图中采样得到有限图，规避离散图优化的固有组合复杂性。
英文摘要
Coordination is a desirable feature in multi-agent systems, ranging from robotic swarms to socioeconomic networks. This paper is concerned with promoting coordination among heterogeneous agents, e.g., machines and humans, interacting in a stag-hunt game. In our model the agents exhibit bounded rationality at different levels, which leads to uncertainty and a propensity for errors during learning and decision-making processes. This paper addresses the problem of designing a network topology that maximizes a global metric of coordination under such constraints. While optimizing over the discrete space of finite graphs is generally computationally intractable, we employ a mean-field approach to lift the problem into the space of graphons. Within this framework, we analyze agents following a logit learning dynamics. Using calculus of variations, we show that for systems with a bimodal rationality profile, it suffices to search for optimal graphons in the ensemble of stochastic block models. We then propose a water-filling algorithm to find a locally optimal graphon. Finite graphs can then be sampled from the optimized graphon, bypassing the inherent combinatorial complexities of discrete graph optimization.
