In randomized experiments, the classic stable unit treatment value assumption (SUTVA) states that the outcome for one experimental unit does not depend on the treatment assigned to other units. However, the SUTVA assumption is often violated in applications such as online marketplaces and social networks where units interfere with each other. We consider the estimation of the average treatment effect in a network interference model using a mixed randomization design that combines two commonly used experimental methods: Bernoulli randomized design, where treatment is independently assigned for each individual unit, and cluster-based design, where treatment is assigned at an aggregate level. Essentially, a mixed randomization experiment runs these two designs simultaneously, allowing it to better measure the effect of network interference. We propose an unbiased estimator for the average treatment effect under the mixed design and show the variance of the estimator is bounded by $O({d^2}n^{-1}p^{-1})$ where $d$ is the maximum degree of the network, $n$ is the network size, and $p$ is the probability of treatment. We also establish a lower bound of $\Omega(d^{1.5}n^{-1}p^{-1})$ for the variance of any mixed design. For a family of sparse networks characterized by a growth constant $\kappa \leq d$, we improve the upper bound to $O({\kappa^7 d}n^{-1}p^{-1})$. Furthermore, when interference weights on the edges of the network are unknown, we propose a weight-invariant design that achieves a variance bound of $O({d^3}n^{-1}p^{-1})$.

翻译：在随机实验中，经典稳定单元处理值假设（SUTVA）规定单个实验单元的结局不依赖于其他单元所接受的处理。然而，在在线市场平台和社交网络等应用中，单元之间会相互干扰，SUTVA 假设常被违反。本文考虑采用混合随机化设计来估计网络干扰模型中的平均处理效应，该设计结合了两种常用实验方法：伯努利随机化设计（独立为每个个体单元分配处理）与基于聚类的设计（在聚合层面分配处理）。本质上，混合随机化实验同时运行这两种设计，从而能更有效地测量网络干扰的效应。我们提出了混合设计下平均处理效应的无偏估计量，并证明其方差上界为 $O({d^2}n^{-1}p^{-1})$，其中 $d$ 为网络最大度，$n$ 为网络规模，$p$ 为处理分配概率。同时，我们建立了任意混合设计方差的下界 $\Omega(d^{1.5}n^{-1}p^{-1})$。对于由增长常数 $\kappa \leq d$ 刻画的一类稀疏网络，我们将方差上界改进至 $O({\kappa^7 d}n^{-1}p^{-1})$。进一步，当网络边上的干扰权重未知时，我们提出一种权重不变设计，其方差界可达 $O({d^3}n^{-1}p^{-1})$。