The R-learner has been popular in causal inference as a flexible and efficient meta-learning approach for heterogeneous treatment effect estimation. In this article, we show the identifiability transition of the generalized R-learning framework from a binary treatment to continuous treatment. To resolve the non-identification issue with continuous treatment, we propose a novel identification strategy named T-identification, acknowledging the use of Tikhonov regularization rooted in the nonlinear functional analysis. Following the new identification strategy, we introduce an $\ell_2$-penalized R-learner framework to estimate the conditional average treatment effect with continuous treatment. The new R-learner framework accommodates modern, flexible machine learning algorithms for both nuisance function and target estimand estimation. Asymptotic properties are studied when the target estimand is approximated by sieve approximation, including general error bounds, asymptotic normality, and inference. Simulations illustrate the superior performance of our proposed estimator. An application of the new method to the medical information mart for intensive care data reveals the heterogeneous treatment effect of oxygen saturation on survival in sepsis patients.

翻译：R-Learner在作为不同治疗效果估计不同治疗效果的灵活而有效的元学习方法的因果推断方法中受到欢迎。在本条中,我们展示了普遍R-学习框架从二进治疗到连续治疗的可识别性过渡。为解决非身份问题,我们提议了一个名为T-身份的新型识别战略,以持续治疗解决非身份问题,我们提议了一个名为T-身份的新型识别战略,承认使用源于非线性功能分析的非线性功能分析的Tikhonov正规化;在新的识别战略之后,我们引入了一个以$ell__2美元为标准血化的R-learner框架,以估计持续治疗的有条件平均治疗效果。新的R-learner框架包含普遍R-learner通用学习框架,从二元治疗转向连续治疗,从普通学习框架的二元治疗到连续治疗;为解决非身份问题,我们提议了一个名为T-身份的连续治疗问题,我们建议采用名为T-lear-lener框架,承认使用源于非线功能分析的非线功能分析的Tkh近近点,包括一般误界点,包括一般误界,以示性正常正常正常、模拟和推断。模拟模拟模拟测算的模拟测算中,我们拟议估测测测测测测算的优点的新的方法用于病人求求生存的求求求求求求求的求求求求的求的求的求求的求的求的求求求求的求的求,在S的求求求求求求的求求求求求求的求的求求求求求求求求求求求求求求求求求求求的求的求的求的求的求的解后,将新方法应用。