We propose an optimal algorithm for estimating conditional average treatment effects (CATEs) when response functions lie in a reproducing kernel Hilbert space (RKHS). We study settings in which the contrast function is structurally simpler than the nuisance functions: (i) it lies in a lower-complexity RKHS with faster eigenvalue decay, (ii) it satisfies a source condition relative to the nuisance kernel, or (iii) it depends on a known low-dimensional covariate representation. We develop a unified two-stage kernel ridge regression (KRR) method that attains minimax rates governed by the complexity of the contrast function rather than the nuisance class, in terms of both sample size and overlap. We also show that a simple model-selection step over candidate contrast spaces and regularization levels yields an oracle inequality, enabling adaptation to unknown CATE regularity.

翻译：本文提出了一种估计条件平均处理效应（CATE）的最优算法，适用于响应函数位于再生核希尔伯特空间（RKHS）的情形。我们研究对比函数在结构上比干扰函数更简单的几种设定：（i）对比函数位于特征值衰减更快的低复杂度RKHS中；（ii）相对于干扰核满足某种源条件；或（iii）依赖于已知的低维协变量表示。我们提出了一种统一的两阶段核岭回归（KRR）方法，该方法在样本量和重叠性方面均能达到由对比函数复杂度（而非干扰函数类）决定的最小最大收敛速率。我们还证明，通过对候选对比空间和正则化水平进行简单的模型选择步骤，可以获得一个oracle不等式，从而实现对未知CATE正则性的自适应。