Where to Experiment? Site Selection Under Distribution Shift via Optimal Transport and Wasserstein DRO

Thomas M. Menino Convention & Exhibition Center 

ow should researchers select experimental sites when the deployment population may differ from observed data? I formulate the problem of experimental site selection as an \textit{optimal transport problem}, developing methods to minimize downstream estimation error by choosing sites that minimize the Wasserstein distance between population and sample covariate distributions. I develop new theoretical upper bounds on PATE and CATE estimation errors, and show that these different objectives lead to different site selection strategies. I extend this approach by using Wasserstein Distributionally Robust Optimization to develop a site selection procedure robust to adversarial perturbations of covariate information: a specific model of distribution shift. I also propose a novel data-driven procedure for selecting the uncertainty radius the Wasserstein DRO problem, which allows the user to benchmark robustness levels against observed variation in their data. Simulation evidence, and a reanalysis of a randomized microcredit experiment in Morocco (Crepon et al.), show that these methods outperform random and stratified sampling of sites when covariates have prognostic $R^2 > .5$, and alternative optimization methods i) for moderate-to-large size problem instances ii) when covariates are moderately informative about treatment effects, and iii) under induced distribution shift.

Causal inference

Optimization

Optimal transport

Distribution Shift