Batched Adaptive Network Formation

Networks are central to many economic and organizational applications, including workplace team formation, social platform recommendations, and classroom friendship development. In these settings, networks are modeled as graphs, with agents as nodes, agent pairs as edges, and edge weights capturing pairwise production or interaction outcomes. This paper develops an adaptive, or \textit{online}, policy that learns to form increasingly effective networks as data accumulates over time, progressively improving total network output measured by the sum of edge weights. Our approach builds on the weighted stochastic block model (WSBM), which captures agents' unobservable heterogeneity through discrete latent types and models their complementarities in a flexible, nonparametric manner. We frame the online network formation problem as a non-standard \textit{batched multi-armed bandit}, where each type pair corresponds to an arm, and pairwise reward depends on type complementarity. This strikes a balance between exploration -- learning latent types and complementarities -- and exploitation -- forming high-weighted networks. We establish two key results: a \textit{batched local asymptotic normality} result for the WSBM and an asymptotic equivalence between maximum likelihood and variational estimates of the intractable likelihood. Together, they provide a theoretical foundation for treating variational estimates as normal signals, enabling principled Bayesian updating across batches. The resulting posteriors are then incorporated into a tailored maximum-weight matching problem to determine the policy for the next batch. Simulations show that our algorithm substantially improves outcomes within a few batches, yields increasingly accurate parameter estimates, and remains effective even in nonstationary settings with evolving agent pools.