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Batched Adaptive Network Formation

Yan Xu, Bo Zhou

arXiv 25 Jul 2025 · Econometrics

arXiv:2507.18961 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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 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 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 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.

Citation extraction

37
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Xu, Y., Hu, M., Chu, J., and Ching, A. T (2024) Heterogeneous Complementarity and Team Design: The Case of Real Estate Agents self1.00084100%
2Bonhomme, S (2021) Teams: Heterogeneity, sorting, and complementarity1.00073100%
3Hirano, K. and Porter, J. R (2025) Asymptotic representations for sequential decisions, adaptive experiments, and batched bandits0.92843100%
4Bickel, P., Choi, D., Chang, X., and Zhang, H (2013) Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels0.84310560%
5Auer, P (2002) Using confidence bounds for exploitation-exploration trade-offs0.84333100%
6Lai, T. L. and Robbins, H (1985) Asymptotically efficient adaptive allocation rules0.84333100%
7Thompson, W. R (1933) On the likelihood that one unknown probability exceeds another in view of the evidence of two samples0.84333100%
8Van der Vaart, A. W (2000) Asymptotic statistics0.7374275%
9Bickel, P. J. and Chen, A (2009) A nonparametric view of network models and Newman–Girvan and other modularities0.7373367%
10Rohrer, J. M., Keller, T., and Elwert, F (2021) Proximity can induce diverse friendships: A large randomized classroom experiment0.73732100%

Showing the top 10 of 37 scored citations.