# Synthetic Design: An Optimization Approach to Experimental Design with Synthetic Controls

arXiv: https://arxiv.org/abs/2112.00278 · HTML: https://mlsanity.com/paper/2112.00278/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls](https://mlsanity.com/paper/1712.09089/) (2017)
- [A Design-Based Perspective on Synthetic Control Methods](https://mlsanity.com/paper/2101.09398/) (2021)
- [Synthetic Controls for Experimental Design](https://mlsanity.com/paper/2108.02196/) (2021)

## Built on by (most cited first, 3 of 3)

- [Adaptive Experiment Design with Synthetic Controls](https://mlsanity.com/paper/2401.17205/) (2024)
- [Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls](https://mlsanity.com/paper/2211.15241/) (2022)
- [Experimental Design for Multi-Channel Imaging via Task-Driven Feature Selection](https://mlsanity.com/paper/2210.06891/) (2022)

## Abstract (arXiv)

We investigate the optimal design of experimental studies that have pre-treatment outcome data available. The average treatment effect is estimated as the difference between the weighted average outcomes of the treated and control units. A number of commonly used approaches fit this formulation, including the difference-in-means estimator and a variety of synthetic-control techniques. We propose several methods for choosing the set of treated units in conjunction with the weights. Observing the NP-hardness of the problem, we introduce a mixed-integer programming formulation which selects both the treatment and control sets and unit weightings. We prove that these proposed approaches lead to qualitatively different experimental units being selected for treatment. We use simulations based on publicly available data from the US Bureau of Labor Statistics that show improvements in terms of mean squared error and statistical power when compared to simple and commonly used alternatives such as randomized trials.