A smoothed Q‐learning algorithm for estimating optimal dynamic treatment regimes
提出一种平滑Q学习算法，用于估计最优动态治疗方案，解决了传统Q学习在非正则推断下的问题，使估计量渐近正态且方差可一致估计，并通过模拟和CATIE-AD数据验证。
Abstract In this paper, we propose a smoothed Q ‐learning algorithm for estimating optimal dynamic treatment regimes. In contrast to the Q ‐learning algorithm in which nonregular inference is involved, we show that, under assumptions adopted in this paper, the proposed smoothed Q ‐learning estimator is asymptotically normally distributed even when the Q ‐learning estimator is not and its asymptotic variance can be consistently estimated. As a result, inference based on the smoothed Q ‐learning estimator is standard. We derive the optimal smoothing parameter and propose a data‐driven method for estimating it. The finite sample properties of the smoothed Q ‐learning estimator are studied and compared with several existing estimators including the Q ‐learning estimator via an extensive simulation study. We illustrate the new method by analyzing data from the Clinical Antipsychotic Trials of Intervention Effectiveness–Alzheimer's Disease (CATIE‐AD) study.