To minimize the mean squared error (MSE) in global average treatment effect (GATE) estimation under network interference, a popular approach is to use a cluster-randomized design. However, in the presence of homophily, which is common in social networks, cluster randomization can instead increase the MSE. We develop a novel potential outcomes model that accounts for interference, homophily, and heterogeneous variation. In this setting, we establish a framework for optimizing designs for worst-case MSE under the Horvitz-Thompson estimator. This leads to an optimization problem over the covariance matrices of the treatment assignment, trading off interference, homophily, and robustness. We frame and solve this problem using two complementary approaches. The first involves formulating a semidefinite program (SDP) and employing Gaussian rounding, in the spirit of the Goemans-Williamson approximation algorithm for MAXCUT. The second is an adaptation of the Gram-Schmidt Walk, a vector-balancing algorithm which has recently received much attention. Finally, we evaluate the performance of our designs through various experiments on simulated network data and a real village network dataset.

翻译：为最小化网络干扰下全局平均处理效应（GATE）估计的均方误差（MSE），一种常用方法是采用聚类随机化设计。然而，在社交网络中普遍存在的同质性现象下，聚类随机化反而可能增大MSE。本文构建了一个新颖的潜在结果模型，该模型综合考虑了网络干扰、同质性与异质性变异。在此框架下，我们建立了基于霍维茨-汤普森估计量的最坏情况MSE设计优化体系，从而将问题转化为在治疗分配协方差矩阵空间中的优化问题，实现了干扰性、同质性与鲁棒性之间的权衡。我们通过两种互补方法对该问题进行建模与求解：第一种方法借鉴MAXCUT问题的Goemans-Williamson近似算法思想，构建半定规划（SDP）模型并采用高斯舍入技术；第二种方法改编了近期备受关注的向量平衡算法——格拉姆-施密特游走算法。最后，我们通过模拟网络数据和真实村庄网络数据集上的多组实验，对所提出设计的性能进行了系统评估。