The performance of A/B testing in both online and offline experimental settings hinges on mitigating network interference and achieving covariate balancing. These experiments often involve an observable network with identifiable clusters, and measurable cluster-level and individual-level attributes. Exploiting these inherent characteristics holds potential for refining experimental design and subsequent statistical analyses. In this article, we propose a novel cluster-adaptive network A/B testing procedure, which contains a cluster-adaptive randomization (CLAR) and a cluster-adjusted estimator (CAE) to facilitate the design of the experiment and enhance the performance of ATE estimation. The CLAR sequentially assigns clusters to minimize the Mahalanobis distance, which further leads to the balance of the cluster-level covariates and the within-cluster-averaged individual-level covariates. The cluster-adjusted estimator (CAE) is tailored to offset biases caused by network interference. The proposed procedure has the following two folds of the desirable properties. First, we show that the Malanobis distance calculated for the two levels of covariates is $O_p(m^{-1})$, where $m$ represents the number of clusters. This result justifies the simultaneous balance of the cluster-level and individual-level covariates. Under mild conditions, we derive the asymptotic normality of CAE and demonstrate the benefit of covariate balancing on improving the precision for estimating ATE. The proposed A/B testing procedure is easy to calculate, consistent, and achieves higher accuracy. Extensive numerical studies are conducted to demonstrate the finite sample property of the proposed network A/B testing procedure.

Users linked together through a network often tend to have similar behaviors. This phenomenon is usually known as network interaction. Users' characteristics, the covariates, are often correlated with their outcomes. Therefore, one should incorporate both the covariates and the network information in a carefully designed randomization to improve the estimation of the average treatment effect (ATE) in network A/B testing. In this paper, we propose a new adaptive procedure to balance both the network and the covariates. We show that the imbalance measures with respect to the covariates and the network are $O_p(1)$. We also demonstrate the relationships between the improved balances and the increased efficiency in terms of the mean square error (MSE). Numerical studies demonstrate the advanced performance of the proposed procedure regarding the greater comparability of the treatment groups and the reduction of MSE for estimating the ATE.

Units in online A/B tests are often involved in social networks. Thus, their outcomes may depend on the treatment of their neighbors. Many of such networks exhibit certain cluster structures allowing the use of these features in the design to reduce the bias from network interference. When the average treatment effect (ATE) is considered from the individual perspective, conditions for the valid estimation restrict the use of these features in the design. We show that such restrictions can be alleviated if the ATE from the cluster perspective is considered. Using an illustrative example, we further show that the weights employed by the Horvitz-Thompson estimator may not appropriately accommodate the network structure, and purely relying on graph-cluster randomization may generate very unbalanced cluster-treated structures across the treatment arms. The measures of such structures for one cluster may depend on the treatment of other clusters and pose a great challenge for the design of A/B tests. To address these issues, we propose a rerandomized-adaptive randomization to balance the clusters and a cluster-adjusted estimator to alleviate the problem of the weights. Numerical studies are conducted to demonstrate the usage of the proposed procedure.