In randomized experiments, the classic Stable Unit Treatment Value Assumption (SUTVA) posits that the outcome for one experimental unit is unaffected by the treatment assignments of other units. However, this assumption is frequently violated in settings such as online marketplaces and social networks, where interference between units is common. We address the estimation of the total treatment effect in a network interference model by employing a mixed randomization design that combines two widely used experimental methods: Bernoulli randomization, where treatment is assigned independently to each unit, and cluster-based randomization, where treatment is assigned at the aggregate level. The mixed randomization design simultaneously incorporates both methods, thereby mitigating the bias present in cluster-based designs. We propose an unbiased estimator for the total treatment effect under this mixed design and show that its variance is bounded by $O(d^2 n^{-1} p^{-1} (1-p)^{-1})$, where $d$ is the maximum degree of the network, $n$ is the network size, and $p$ is the treatment probability. Additionally, we establish a lower bound of $\Omega(d^{1.5} n^{-1} p^{-1} (1-p)^{-1})$ for the variance of any mixed design. Moreover, when the interference weights on the network's edges are unknown, we propose a weight-invariant design that achieves a variance bound of $O(d^3 n^{-1} p^{-1} (1-p)^{-1})$, which is aligned with the estimator introduced by Cortez-Rodriguez et al. (2023) under similar conditions.

翻译：在随机实验中，经典的稳定单元处理值假设（SUTVA）假定一个实验单元的结果不受其他单元处理分配的影响。然而，这一假设在在线市场和社交网络等场景中经常被违背，其中单元间的干扰普遍存在。我们通过采用一种混合随机化设计来估计网络干扰模型中的总处理效应，该设计结合了两种广泛使用的实验方法：伯努利随机化（即对每个单元独立分配处理）和基于聚类的随机化（即在聚合层面分配处理）。混合随机化设计同时融合了这两种方法，从而减轻了基于聚类的设计中存在的偏差。我们为此混合设计提出了一个总处理效应的无偏估计量，并证明其方差上界为 $O(d^2 n^{-1} p^{-1} (1-p)^{-1})$，其中 $d$ 为网络的最大度，$n$ 为网络规模，$p$ 为处理概率。此外，我们建立了任意混合设计方差的下界 $\Omega(d^{1.5} n^{-1} p^{-1} (1-p)^{-1})$。进一步地，当网络边上的干扰权重未知时，我们提出了一种权重不变的设计，其方差上界为 $O(d^3 n^{-1} p^{-1} (1-p)^{-1})$，这与 Cortez-Rodriguez 等人（2023）在类似条件下提出的估计量相一致。