Structure-Adaptive Estimation of Heterogeneous Treatment Effects with Kernel Methods

We study conditional average treatment effect (CATE) estimation from observational data in regimes with potentially weak overlap, when the nuisance response functions lie in a reproducing kernel Hilbert space (RKHS), but the contrast function is structurally simpler. We consider three forms of such simplicity: (i) membership in a lower-complexity RKHS with faster eigenvalue decay, (ii) a source condition relative to the nuisance kernel, or (iii) dependence on a known low-dimensional covariate representation. We develop a unified two-stage kernel ridge regression procedure that remains valid under weak overlap and attains minimax rates determined by the complexity of the contrast function. Unlike existing methods that rely on propensity-score estimation and stronger nuisance error control, our procedure avoids propensity-score estimation altogether and requires only that the outcome nuisance class be well specified, which is especially advantageous under weak overlap. We also show that a simple model-selection step over candidate contrast spaces and regularization levels satisfies an oracle inequality, enabling adaptation to unknown CATE regularity.