Description:

Abhishek Ananth (Emory): Optimal Treatment Assignment Rules on Networked Populations

Abstract: I address the challenge of optimally distributing treatments among units in a population while considering interference across units, which is governed by a network of interactions. Within my framework, a planner aims to allocate a limited number of treatments among units in a target population to maximize a welfare measure.

To derive an empirical welfare maximizing treatment assignment rule (EWM rule), the planner utilizes data from a (quasi) experiment conducted on a separate and independent pilot population. In this paper, I extend empirical welfare maximization to incorporate interference, resulting in a rule that translates observed data from the pilot population into treatment assignments at the population level in the target population. I demonstrate that previously explored individual-level treatment assignments are effectively constrained population-level treatment assignments.

I offer finite sample bounds for the regret associated with the EWM rule, imposing restrictions on both the shape of the network and the nature of interference. This regret measures the disparity between the maximum feasible welfare and the welfare achieved by the EWM rule.

The main conclusion is that the regret linked with the EWM rule, extended to account for interference, converges at the parametric rate (with a logarithmic factor) as the size of the pilot population increases. Furthermore, I demonstrate that no statistical treatment rule achieves a faster rate of convergence for the uniform regret, suggesting that the EWM rule is rate-optimal.