Optimal Transport Learning: Balancing Value Optimization and Fairness in Individualized Treatment Rules

TL;DR

This paper introduces a novel optimal transport-based method to create fair individualized treatment rules that balance value maximization with demographic fairness, supported by theoretical bounds and empirical validation.

Contribution

It proposes a flexible framework for transforming and balancing ITRs for fairness and value, including a new trade-off approach with theoretical guarantees.

Findings

The method effectively enforces demographic parity in ITRs.

The trade-off parameter allows tuning between fairness and value.

Empirical results show improved fairness without significant value loss.

Abstract

Individualized treatment rules (ITRs) have gained significant attention due to their wide-ranging applications in fields such as precision medicine, ridesharing, and advertising recommendations. However, when ITRs are influenced by sensitive attributes such as race, gender, or age, they can lead to outcomes where certain groups are unfairly advantaged or disadvantaged. To address this gap, we propose a flexible approach based on the optimal transport theory, which is capable of transforming any optimal ITR into a fair ITR that ensures demographic parity. Recognizing the potential loss of value under fairness constraints, we introduce an ``improved trade-off ITR," designed to balance value optimization and fairness while accommodating varying levels of fairness through parameter adjustment. To maximize the value of the improved trade-off ITR under specific fairness levels, we propose a smoothed fairness constraint for estimating the adjustable parameter. Additionally, we establish a theoretical upper bound on the value loss for the improved trade-off ITR. We demonstrate performance of the proposed method through extensive simulation studies and application to the Next 36 entrepreneurial program dataset.