Efficient Balanced Treatment Assignments for Experimentation

TL;DR

This paper introduces an optimal treatment assignment algorithm based on two-sample test optimization, improving experimental balance and efficacy through a novel probabilistic and transductive inference framework.

Contribution

It presents a polynomial-time optimal assignment algorithm using a two-sample test perspective and a new formulation of estimation as transductive inference.

Findings

Improved balance in treatment groups in simulations

Algorithm is optimal with respect to the minimum spanning tree test

Demonstrates enhanced efficacy over existing methods

Abstract

In this work, we reframe the problem of balanced treatment assignment as optimization of a two-sample test between test and control units. Using this lens we provide an assignment algorithm that is optimal with respect to the minimum spanning tree test of Friedman and Rafsky (1979). This assignment to treatment groups may be performed exactly in polynomial time. We provide a probabilistic interpretation of this process in terms of the most probable element of designs drawn from a determinantal point process which admits a probabilistic interpretation of the design. We provide a novel formulation of estimation as transductive inference and show how the tree structures used in design can also be used in an adjustment estimator. We conclude with a simulation study demonstrating the improved efficacy of our method.