Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines. We jointly infer the weight matrix of the network and the interaction kernel, which determine respectively which agents interact with which others and the rules of such interactions from data consisting of multiple trajectories. The estimator we propose leads naturally to a non-convex optimization problem, and we investigate two approaches for its solution: one is based on the alternating least squares (ALS) algorithm; another is based on a new algorithm named operator regression with alternating least squares (ORALS). Both algorithms are scalable to large ensembles of data trajectories. We establish coercivity conditions guaranteeing identifiability and well-posedness. The ALS algorithm appears statistically efficient and robust even in the small data regime but lacks performance and convergence guarantees. The ORALS estimator is consistent and asymptotically normal under a coercivity condition. We conduct several numerical experiments ranging from Kuramoto particle systems on networks to opinion dynamics in leader-follower models.

翻译：网络上的多智能体系统建模是众多学科领域中的一项基本挑战。我们联合推断网络的权重矩阵和相互作用核，其中权重矩阵决定哪些智能体与哪些其他智能体相互作用，而相互作用核则决定此类相互作用的规则，所用数据由多条轨迹组成。我们提出的估计量自然引出一个非凸优化问题，并研究了两种求解方法：一种基于交替最小二乘(ALS)算法；另一种基于名为算子回归与交替最小二乘(ORALS)的新算法。两种算法均可扩展到大数据轨迹集合。我们建立了保证可辨识性和适定性的强制条件。ALS算法即使在数据量较小时也表现出统计效率和鲁棒性，但缺乏性能和收敛保证。ORALS估计量在强制条件下具有一致性和渐近正态性。我们进行了多项数值实验，涵盖网络上的Kuramoto粒子系统以及领导者-追随者模型中的观点动力学。