Fairness-Oriented Deep Learning for Distributionally Robust Optimal Individualized Treatment Regime

There has been a growing interest in developing advanced methodologies aimed at estimating optimal individualized treatment regimes (ITRs) in fields such as precision medicine, clinical decision making, and healthcare resource allocation. Incorporating individual characteristics into decision-making processes offers significant potential for improving treatment efficiency and precision. However, many existing methods impose specific structural assumptions on the decision function, which can lead to model misspecification and erroneous conclusions. Moreover, traditional frameworks often assume that training and testing distributions are identical, limiting the generalizability of derived ITRs in practice. To address these limitations, we propose a novel approach that utilizes Wasserstein distributionally robust optimization in conjunction with deep neural networks (DNNs) for estimating the decision function. This method accounts for worst-case scenarios across a spectrum of probability distributions that are close to a nominal distribution in terms of Wasserstein distance. Unlike conventional linear or nonlinear models, DNNs provide the capacity to navigate high-dimensional covariates effectively, allowing for robust modeling of complex relationships between covariates and The implementation of ITRs within societal contexts raises significant concerns regarding potential discrimination and fairness. Many prevailing fairness-oriented strategies focus on achieving balanced rewards or navigating trade-offs among various demographic groups, yet it is imperative to ensure equitable access to medical resources for minority or disadvantaged populations. To address these concerns, we introduce the concept of Demographic Parity ITR (DP-ITR), where policy decisions are made independently of sensitive attributes. We propose three fairness approaches that utilize distributionally robust optimization and DNNs for estimating the decision function. The first method applies optimal transport theory to map optimal policies to fair policies. The second method considers covariance between the decision function and sensitive attributes as a measure of correlation strength, allowing for customization. The third method ensures complete independence between the decision function and sensitive attributes. Collectively, these strategies aim to enhance equitable decision-making while optimizing overall policy effectiveness. We will thoroughly analyze the theoretical properties of our proposed estimators, including regret bounds, consistency, and convergence rates. Additionally, we will conduct extensive numerical studies including simulations and applications to realworld datasets, to evaluate their performance. This framework offers a robust and flexible approach to decision function estimation, integrating fairness considerations and contributing to the advancement of individualized decision making.