In consequential domains, it is often impossible to compel individuals to
take treatment, so that optimal policy rules are merely suggestions in the
presence of human non-adherence to treatment recommendations. In these same
domains, there may be heterogeneity both in who responds in taking-up
treatment, and heterogeneity in treatment efficacy. While optimal treatment
rules can maximize causal outcomes across the population, access parity
constraints or other fairness considerations can be relevant in the case of
encouragement. For example, in social services, a persistent puzzle is the gap
in take-up of beneficial services among those who may benefit from them the
most. When in addition the decision-maker has distributional preferences over
both access and average outcomes, the optimal decision rule changes. We study
causal identification, statistical variance-reduced estimation, and robust
estimation of optimal treatment rules, including under potential violations of
positivity. We consider fairness constraints such as demographic parity in
treatment take-up, and other constraints, via constrained optimization. Our
framework can be extended to handle algorithmic recommendations under an
often-reasonable covariate-conditional exclusion restriction, using our
robustness checks for lack of positivity in the recommendation. We develop a
two-stage algorithm for solving over parametrized policy classes under general
constraints to obtain variance-sensitive regret bounds. We illustrate the
methods in two case studies based on data from randomized encouragement to
enroll in insurance and from pretrial supervised release with electronic
monitoring.

连同统计可减少方差的估计和鲁棒估计在内，研究了在可能违反正性的情况下的最优治疗规则的因果识别和估计，以及如公平性等约束通过约束优化处理，并提出了用于获得方差敏感性遗憾界的多参数政策类的两阶段算法。

最佳和公平的激励政策评估与学习

Optimal and Fair Encouragement Policy Evaluation and Learning

Individualized treatment rules aim to identify if, when, which, and to whom
treatment should be applied. A globally aging population, rising healthcare
costs, and increased access to patient-level data have created an urgent need
for high-quality estimators of individualized treatment rules that can be
applied to observational data. A recent and promising line of research for
estimating individualized treatment rules recasts the problem of estimating an
optimal treatment rule as a weighted classification problem. We consider a
class of estimators for optimal treatment rules that are analogous to convex
large-margin classifiers. The proposed class applies to observational data and
is doubly-robust in the sense that correct specification of either a propensity
or outcome model leads to consistent estimation of the optimal individualized
treatment rule. Using techniques from semiparametric efficiency theory, we
derive rates of convergence for the proposed estimators and use these rates to
characterize the bias-variance trade-off for estimating individualized
treatment rules with classification-based methods. Simulation experiments
informed by these results demonstrate that it is possible to construct new
estimators within the proposed framework that significantly outperform existing
ones. We illustrate the proposed methods using data from a labor training
program and a study of inflammatory bowel syndrome.

本文介绍了通过重新定义分类问题，将最优治疗规则的估计转化为分类问题，提出了一类新的基于凸大间隔分类器的最优治疗规则估计方法，这类方法具有双重稳健性，能够在使用属性模型或结果模型进行正确说明时一致地估计最优个体化治疗规则，并使用半参数效率理论技术推导了提议的估计器的一致收敛率，并使用这些结果表征了基于分类的方法估计最优治疗规则时的偏差 - 方差折衷，并通过仿真实验证明了在提议的框架内构造的新估计器可以显著优于现有估计器，数据来自劳动培训计划和炎症性肠病研究。