# Optimal block designs for experiments on networks

## TL;DR

This paper introduces a method for designing optimal experiments on networks by extending linear network effects models, using spectral clustering for block formation, and employing exchange algorithms to improve efficiency over traditional designs.

## Contribution

It presents a novel approach combining network-aware block design, spectral clustering, and exchange algorithms to optimize experimental efficiency on network-structured data.

## Key findings

- Optimal designs reduce variance of treatment effect estimators.
- Spectral clustering effectively defines blocks considering network structure.
- Efficiency gains over conventional randomized designs are demonstrated.

## Abstract

We propose a method for constructing optimal block designs for experiments on networks. The response model for a given network interference structure extends the linear network effects model to incorporate blocks. The optimality criteria are chosen to reflect the experimental objectives and an exchange algorithm is used to search across the design space for obtaining an efficient design when an exhaustive search is not possible. Our interest lies in estimating the direct comparisons among treatments, in the presence of nuisance network effects that stem from the underlying network interference structure governing the experimental units, or in the network effects themselves. Comparisons of optimal designs under different models, including the standard treatment models, are examined by comparing the variance and bias of treatment effect estimators. We also suggest a way of defining blocks, while taking into account the interrelations of groups of experimental units within a network, using spectral clustering techniques to achieve optimal modularity. We expect connected units within closed-form communities to behave similarly to an external stimulus. We provide evidence that our approach can lead to efficiency gains over conventional designs such as randomized designs that ignore the network structure and we illustrate its usefulness for experiments on networks.