With the emergence of precision medicine, estimating optimal individualized decision rules (IDRs) has attracted tremendous attention in many scientific areas. Most existing literature has focused on finding optimal IDRs that can maximize the expected outcome for each individual. Motivated by complex individualized decision making procedures and the popular conditional value at risk (CVaR) measure, we propose a new robust criterion to estimate optimal IDRs in order to control the average lower tail of the individuals' outcomes. In addition to improving the individualized expected outcome, our proposed criterion takes risks into consideration, and thus the resulting IDRs can prevent adverse events. The optimal IDR under our criterion can be interpreted as the decision rule that maximizes the ``worst-case" scenario of the individualized outcome when the underlying distribution is perturbed within a constrained set. An efficient non-convex optimization algorithm is proposed with convergence guarantees. We investigate theoretical properties for our estimated optimal IDRs under the proposed criterion such as consistency and finite sample error bounds. Simulation studies and a real data application are used to further demonstrate the robust performance of our methods. Several extensions of the proposed method are also discussed.

翻译：随着精密医学的出现,对最佳个体化决定规则的估计在许多科学领域引起了极大的关注。大多数现有文献侧重于寻找最佳的IDR,以最大限度地实现每个人的预期结果。受复杂的个体化决策程序和受欢迎的有条件风险值(CVaR)衡量的驱动,我们提出了一个新的强健标准,以估计最佳个体化决定规则,从而控制个人结果的平均较低尾巴。除了改进个体化预期成果外,我们提出的标准还考虑到风险,从而可以防止不利事件。根据我们的标准,最佳的IDR可以被解释为在基本分布受限的情况下最大限度地实现个人化结果的“最坏情况”假设的决策规则。提出了高效的非凝固优化算法,并提供了趋同保证。我们根据拟议标准,如一致性和有限的抽样误差,对我们估计的最佳IDR的理论属性进行了调查。我们使用的模拟研究和实际数据应用可以进一步证明我们方法的稳健性表现。还讨论了拟议方法的若干扩展。