# Rate-Optimal Cluster-Randomized Designs for Spatial Interference

arXiv: https://arxiv.org/abs/2111.04219 · HTML: https://mlsanity.com/paper/2111.04219/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2021.

## Built on by (most cited first, 14 of 14)

- [Multi-Armed Bandits with Interference](https://mlsanity.com/paper/2402.01845/) (2024)
- [Online Experimental Design With Estimation-Regret Trade-off Under Network Interference](https://mlsanity.com/paper/2412.03727/) (2024)
- [Linear Contextual Bandits with Interference](https://mlsanity.com/paper/2409.15682/) (2024)
- [Unraveling the Interplay between Carryover Effects and Reward Autocorrelations in Switchback Experiments](https://mlsanity.com/paper/2403.17285/) (2024)
- [Balancing Interference and Correlation in Spatial Experimental Designs: A Causal Graph Cut Approach](https://mlsanity.com/paper/2505.20130/) (2025)
- [Off-policy Evaluation with Deeply-abstracted States](https://mlsanity.com/paper/2406.19531/) (2024)
- [Clustered Switchback Designs for Experimentation Under Spatio-temporal Interference](https://mlsanity.com/paper/2312.15574/) (2023)
- [Causal Deepsets for Off-policy Evaluation under Spatial or Spatio-temporal Interferences](https://mlsanity.com/paper/2407.17910/) (2024)
- [A Two-armed Bandit Framework for A/B Testing](https://mlsanity.com/paper/2507.18118/) (2025)
- [Differences-in-Neighbors for Network Interference in Experiments](https://mlsanity.com/paper/2503.02271/) (2025)
- [Design-Based Bandits Under Network Interference: Trade-Off Between Regret and Statistical Inference](https://mlsanity.com/paper/2510.07646/) (2025)
- [Designing Time Series Experiments in A/B Testing with Transformer Reinforcement Learning](https://mlsanity.com/paper/2602.01853/) (2026)
- [Causal Estimation of User Learning in Personalized Systems](https://mlsanity.com/paper/2306.00485/) (2023)
- [GeoDose-CP: Graph-Local Conformal Inference for Continuous-Treatment Earth Observation](https://mlsanity.com/paper/2609.28895/) (2026)

## Abstract (arXiv)

We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares outcomes under the counterfactuals that all or no units are treated. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz-Thompson estimator that compares the average outcomes of units with all or no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator's rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms.