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：为在网络干扰下最小化全局平均处理效应（GATE）估计的均方误差（MSE），一种常用方法是采用聚类随机设计。然而，在社交网络中常见的同质性存在时，聚类随机化反而可能增加MSE。我们建立了一个新颖的潜在结果模型，该模型同时考虑了干扰效应、同质性以及异质性变异。在此设定下，我们构建了一个基于霍维茨-汤普森估计量的最坏情况MSE设计优化框架，从而导出一个关于处理分配协方差矩阵的优化问题，该问题需要权衡干扰、同质性与鲁棒性。我们通过两种互补方法构建并求解该问题：第一种借鉴了Goemans-Williamson近似算法解决MAXCUT问题的思路，通过构建半定规划（SDP）并结合高斯舍入法求解；第二种则采用近年来备受关注的向量平衡算法——Gram-Schmidt Walk的改进版本。最后，我们通过在模拟网络数据和真实村庄网络数据集上的多组实验，评估了所提出设计的性能。